Abstract
This paper is a survey of the articles reviewed by the journalMatematika from January 1971 through August 1989 on groups of transformations of Riemannian manifolds and their applications.
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Literature cited
B. Abakirov, “Some transformation groups in Riemannian spaces with degeneracy fields,” in:Studies in Topology and Geometry [in Russian], Frunze (1985), pp. 3–6.
B. Abakirov and D. Moldobaev, “Some problems about groups of conformai mappings of Riemannian spaces,”Sb. Tr. Aspirantov i Soiskatelei (Collection of Papers by Graduate Students and Research Assistants), Kirg. Univ. Ser. Mat. Nauk,10, 3–7 (1973).
G. B. Abakirova, “On intransitive groups of conformai mappings in four-dimensional spaces with degeneracy fields,” in:Studies in Topology and Geometry [in Russian], Frunze (1985), pp. 6–14.
D. V. Alekseevskii, “Groups of conformai mappings of Riemannian spaces,”Mat. Sb.,89, No. 2, 280–296 (1972).
D. V. Alekseevskii, “S n andE n are the only Riemannian spaces admitting an essential conformai mapping,”Usp. Mat. Nauk,28, No. 5, 225–226 (1973).
D. V. Alekseevskii, “Holonomy groups and recurrent tensor fields in Lorentz spaces,”Prob. Teorii Gravitatsii i Elementarn. Chastits (Problems of Gravitational and Elementary Particle Theory), No. 5, Atomizdat, Moscow (1974), pp. 5–17.
D. V. Alekseevskii, “Homogeneous Riemannian spaces of negative curvature,”Mat. Sb.,96, No. 1, 93–117 (1975).
D. V. Alekseevskii and B. N. Kimel'fel'd, “The classification of homogeneous conformally flat Riemannian manifolds,Mat. Zametki,24, No. 1, 103–110 (1978).
G. B. Alybakova, “On intransitive groups of conformai mappings of four-dimensional Riemannian spaces with degenerate hypersurfaces,” in:Studies in Topology and Generalized Spaces [in Russian], Frunze (1988), pp. 63–70.
A. V. Aminova, “On gravitational fields admitting groups of projective motions,”Dokl. Akad. Nauk SSSR,197, No. 4, 807–809 (1971).
A. V. Aminova, “Projective groups in gravitational fields. I,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 8, 3–13 (1971).
A. V. Aminova, “Projective groups in gravitational fields. II,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 8, 14–20 (1971).
A. V. Aminova, “On infinitesimal mappings that preserve the trajectories of test bodies,” [in Russian], Preprint ITF-71-85 R.-Kiev (1971).
A. V. Arninova, “Projective-group properties of some Riemannian spaces,”Tr. Geometr. Seminara, VINITI,6, 295–316 (1974).
A. V. Aminova, “Groups of projective and affine motions in spaces of the general theory of relativity,”Tr. Geometr. Seminara, VINITI,6, 317–346 (1974).
A. V. Arninova, “Projective groups in space-times admitting two constant vector fields,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 10–11, 9–22 (1975–1976).
A. V. Aminova, “On concircular motions in Riemannian spaces,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 10–11, 127–138 (1975–1976).
A. V. Aminova, “The determination of infinitesimal almost projective mappings,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 13, 3–9 (1976).
A. V. Aminova, “Concircular vector fields and group symmetries in universes of constant curvature,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 14–15, 4–16 (1978).
A. V. Aminova, “Examples of groups of almost projective motions,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 14–15, 138–142 (1978).
A. V. Aminova, “Groups of almost projective motions of spaces of affine connection,”Izv. Vuzov, Mat., No. 4, 71–75 (1979).
A. V. Aminova, “Groups of almost projective motions in reducible gravitational fields,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 17, 3–11 (1980).
A. V. Aminova, “On a class of projectively movable spaces. I,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 18, 3–10 (1981).
A. V. Aminova, “On skew-orthogonal frames and certain properties of parallel tensor fields on Riemannian manifolds,”Izv. Vuzov. Mat., No. 6, 63–67 (1982).
A. V. Aminova, “On a moving skew-orthogonal frame and a type of projective motion of Riemannian manifolds,”Izv. Vuzov. Mat., No. 9, 69–74 (1982).
A. V. Aminova, “On the Eisenhart equation and the first integrals of the equations of geodesies in Riemannian manifolds of Lorentz signature,”Izv. Vuzov. Mat., No. 1, 12–26 (1983).
A. V. Aminova, “On the projective-group properties of Riemannian spaces of Lorentz signature,”Izv. Vuzov. Mat., No. 6, 10–21 (1984).
A. V. Aminova, “Nonhomothetic projective motions in ordinaryh-spaces of Lorentz signature,”Izv. Vuzov. Mat., No. 4, 3–13 (1985).
A. V. Aminova, “Lie algebras of projective motions and mechanical conservation laws in two-dimensional universes of special structure,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 22, 3–12 (1985).
A. V. Aminova, “A surface of revolution as a dynamic model of a Lagrangian system with one degree of freedom. Conserved quantities,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 22, 12–30 (1985).
A. V. Aminova, “Lie algebras of projective motions in h-spaces of type (3),”Izv. Vuzov. Mat., No. 3, 68–71 (1987).
A. V. Aminova, “On the projective-group symmetries of Friedman universes and their multidimensional generalizations—ordinaryh-spaces of type {1(1...1)},”Izv. Vuzov. Mat., No. 12, 66–68 (1987).
A. V. Aminova, “On the integration of a first-order covariant differential equation and geodesic mappings of Riemannian spaces of arbitrary signature and dimension,”Izv. Vuzov. Mat., No. 1, 3–13 (1988).
A. V. Aminova, “Symmetry groups in the general theory of relativity,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 25, 16–23 (1988).
A. V. Aminova, “Lie algebras of projective motions of ordinaryh-spaces of Lorentz signature,”Izv. Vuzov. Mat., No. 1, 3–12 (1989).
A. V. Aminova, “On invariance groups of the equations of motion of test bodies of isotropic cosmological models,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 26, 93–101 (1989).
A. V. Aminova and Yu. V. Monakhov, “The unified nonsymmetric field theories of Einstein, Bonnor, and Schrödinger in a space with symmetries,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 12, 3–16 (1977).
A. V. Aminova and A. M. Mukhamedov, “Groups of almost projective motions in De Sitter space,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 16, 3–8 (1980).
A. V. Aminova and A. M. Mukhamedov, “Groups of almost projective motions ofn-dimensional (pseudo)-Euclidean spaces,”Izv. Vuzov. Mat., No. 11, 5–11 (1980).
A. V. Aminova and T. P. Toguleva, “Projective and affine motions determined by concircular vector fields,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 10–11, 139–153 (1975–1976).
V. V. Astrakhantsev, “On holonomy groups of four-dimensional pseudo-Riemannian spaces,”Mat. Zametki,9, 59–66 (1971).
V. V. Astrakhantsev, “Pseudo-Riemannian symmetric spaces with commutative holonomy group,”Mat. Sb.,90, No. 2, 288–305 (1973).
R. F. Bilyalov, “Conformai transformation groups in gravitational fields,”Dokl. Akad. Nauk SSSR,152, No. 3, 570–572 (1963).
O. I. Bogoyavlenskii and S. P. Novikov, “The qualitative theory of homogeneous cosmological models,”Tr. Seminara im. I. G. Petrovskogo, Moscow University, No. 1, 7–43 (1975).
D. V. Volkov, D. P. Sorokin, and V. I. Tkach, “Gauge fields in mechanisms of spontaneous compactification of subspaces,”Teor, i mat. fiz.,56, No. 2, 171–179 (1983).
N. V. Volkov, “The local group of motions of ann-dimensional quasiorthogonal Riemannian spacetime” [in Russian],Leningrad Electrotechnical Institute (1979).
E. I. Galyarskii, “Two-dimensional groups of conformai symmetry and their generalizations,”Sovr. Vopr. Prikl. Mat. i Programmir. Mat. Nauki (Modern Questions of Applied Mathematics and Programming. Mathematical Sciences), Kishinev (1979), pp. 31–36.
O. S. Germanov, “On three-dimensional Riemannian spaces admitting a group of conformai transformations of order at most three” [in Russian]Gor'kii Polyt. Inst. (1986).
V. P. Golubyatnikov and L. N. Pestov, “On a group of conformai mappings ofR3 in stellar dynamics and the inverse kinematical problems of seismics,” in:Priblizhen. Metody Resheniya i Vopr. Korrektnosti Obratn. Zadach. (Approximate Methods of Solution and Questions of the Well-posedness of Inverse Problems), Novosibirsk (1981), pp. 35–43.
I. V. Gribkov, “On sufficient conditions for maximality of holonomy groups of Riemannian manifolds,”Vestn. MGU. Mat. Mekh., No. 3, 50–52 (1988).
N. A. Gromov, “On passage to the limit in sets of groups of motions and the Lie algebras of spaces of constant curvature,”Mat. Zametki,32, No. 3, 355–364 (1982).
R. A. Daishev,Isometric Motions of an Ideal Fluid with a Massive Scalar Field [in Russian], Kazan University Press (1983).
R. A. Daishev, “Isometric motions of an ideal fluid with massive scalar field,”Gravitation and the Theory of Relativity [in Russian], Kazan Univ., No. 25, 40–57 (1988).
B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko,Modern Geometry. Methods and Applications [in Russian], 2nd Ed., revised, Nauka, Moscow (1986).
A. I. Egorov and L. I. Egorova, “On some spaces that admit groups of motions of maximal order,”Liet. mat. rinkinys (Lithuanian Mathematical Collection),12, No. 2, 39–42 (1972).
I. P. Egorov, “Automorphisms in generalized spaces,”Itogi Nauki i Tekhniki, Ser. Probl. Geom.,10, 147–191 (1980).
L. I. Zhukova, “Riemannian spaces with projective group,”Uch. Zap. Penz. Fed. Inst.,124, 13–18 (1971).
L. I. Zhukova, “Projective mappings in Riemannian spaces (the isotropic case),”Uch. Zap. Penz. Ped. Inst.,124, 19–25 (1971).
L. I. Zhukova, “On groups of projective mappings of certain Riemannian spaces,”Uch. Zap. Penz. Ped. Inst,124, 26–30 (1971).
L. I. Zhukova, “Riemannian spaces admitting projective mappings,”Izv. Vuzov. Mat., No. 6, 37–41 (1973).
G. G. Ivanov, “Isometric motions in space-times with nonlinear scalar fields,”Izv. Vuzov. Mat., No. 2, 77–78 (1985).
G. G. Ivanov, “On the immersion of space-time with isometric and conformai motions,”Izv. Vuzov. Mat., No. 1, 61–63 (1985).
G. G. Ivanov and S. V. Chervon, “Exact solutions in theSO(3)-invariant nonlinear sigma-model connected with isometric and homothetic symmetries,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 24, 37–44 (1987).
V. R. Kaigorodov, “Semisymmetric Lorentz spaces with perfect holonomy group,”Gravitation and the Theory of Relativity [in Russian], Kazan University, No. 14–15, 113–120 (1978).
N. R. Kamyshanskii, “One-parameter groups of motions of pseudo-Riemannian spaces of dimension 2,”Tr. seminara po vektor. i tenzor. anal, s ikh pril. k geom., mekh., i fiz. (Proceedings of the seminar on vector and tensor analysis and their applications to geometry, mechanics, and physics), Moscow State University, No. 19, 218–239 (1979).
N. R. Kamyshanskii, “Classification of the complete simply connected subprojective pseudo-Riemannian spaces of V. F. Kagan,”Tr. seminara po vektor. i tenzor. anal, s ikh pril. k geom., mekh., i fiz. (Proceedings of the seminar on vector and tensor analysis and their applications to geometry, mechanics, and physics), Moscow State University, No. 20, 66–85 (1981).
T. I. Kolesova, “Decomposition of the isotropy group of some homogeneous Riemannian spaces,”Differential geometry and Lie algebras, Mosk. Obi. Ped. Inst. (Moscow Regional Pedagogical Institute), 66–70 (1983).
M. T. Kondaurov, “Motions and affine mappings in symmetric conformally Euclidean spaces” [in Russian], Publication of the JournalIzv. Vuzov. Matematika (1983).
V. G. Kopp, “On invariant groups of infinitesimal motions of a three-dimensional Lorentz space,”Tr. Geom. seminara Kazan. Univ., No. 17, 13–29 (1986).
N. S. Lipatov, “Homothetic immobility in Gödel space,” in:Motions in Generalized Spaces [in Russian], Ryazan (1985), pp. 95–97.
A. A. Lovkov, “On a simply transitive group of homothetic mappings inV 4,”Uch. Zap. Penz. Ped. Inst.,124, 70–72 (1971).
M. A. Malakhal'tsev, “Free motions of the group of isometries on a space whose curvature is of constant sign. The group of isometries and the Ricci tensor” [in Russian], Kazan University (1986).
V. E. Mel'nikov, “On Riemannian spaces that admit a group of motions with decomposable isotropy group,”Izv. Vuzov. Mat., No. 2, 81–89 (1971).
V. E. Mel'nikov, “On groups of rotations of Riemannian spaces,” in:Proc. 27th Sci.-Tech. Conf. Mos. Inst. Radiotec., Electr., and Autom. [in Russian], Moscow (1978), pp. 53–60.
J. Mikes, “On concircular vector fields ‘in the large’ on compact Riemannian spaces” [in Russian], Odessa University (1988).
J. Mikes, “On the existence ofn-dimensional compact Riemannian spaces admitting nontrivial projective mappings ‘in the large’,”Dokl. Akad. Nauk SSSR,305, No. 3, 534–536 (1989).
J. Mikes and S. M. Pokas',Lie groups of mappings of second order in associated Riemannian spaces [in Russian], Odessa University (1981).
G. G. Mikhailichenko, “Three-dimensional Lie algebras of mappings of a plane,”Sib. Mat. Zh.,23, No. 5, 132–141 (1982).
N. V. Mitskevich and Yu. E. Senin, “The topology and isometries of a De Sitter universe,”Dokl. Akad. Nauk SSSR,266, No. 3, 586–590 (1982).
I. M. Mitsnefes and I. A. Undalova, “One-parameter groups of motions of the pseudo-Riemannian space V4,” in:Proc. of the 4th Sci. Conf. Young Scholars Mech./Math. Fac. [in Russian], Gor'kii (1979), pp. 64–71.
D. O. Moldobaev, “On the orders of the groups of conformai mappings in Riemannian spaces,” in:Studies in Integro-Differential Equations [in Russian], No. 16, 313–323 (1983).
D. O. Moldobaev, “On conformally extended groups of motions of Riemannian spaces,” in:Studies in Topological and Generalized Spaces [in Russian], 63–70 (1988).
A. M. Mukhamedov, “Maximally movable gravitational fields with respect to almost projective motions that preserve a quadratic geodesic complex,”Tr. Geom. Seminara Kazan. Univ., No. 11, 64–69 (1979).
S. P. Novikov, “Some problems of gravitational theory,”Usp. Mat. Nauk,28, No. 5, p. 266 (1973).
S. Ya. Nus', “On infinitesimal isometries in the tangent bundle of the homethetically movable Riemannian spaceV 3 andV 4” [in Russian], Kazan University (1985).
M. E. Osinovskii and O. A. Teslenko, “Global analysis of vacuum spaces of third type admitting a twodimensional commutative group of isometries,”Gravitation and the Theory of Relativity [in Russian], Kazan Univ., No. 16, 111–119 (1980).
V. I. Pan'zhenskii, “On motions in a tangent bundle with the Sasaki metric,”Penz. Gos. Ped. Inst. (1989).
A. Z. Petrov,New Methods in the General Theory of Relativity [in Russian], Nauka, Moscow (1966).
S. M. Pokas',Motions in Associated Riemannian Spaces [in Russian], Odessa University (1980).
S. M. Pokas',Infinitesimal Conformai Mappings in Associated Riemannian Spaces of Second Order [in Russian], Odessa University (1981).
V. A. Popov, “Extensibility of local isometry groups,”Mat. Sb.,135, No. 1, 12–13 (1988).
K. Riives, “Lie subgroups of motions of the Euclidean spaceR 5 and their orbits. II,”Tartu Ülikooli toimetised (Tartu University Reports), No. 342, 83–109 (1974).
N. R. Sibgatullin, “On the theory of the neutron electrovacuum with Abelian group of motionsg 2 on V2,”Vestn. MGU. Mat.-Mekh., No. 2, 44–51 (1985).
N. S. Sinyukov, “Infinitesimal almost-geodesic mappings of affinely connected and Riemannian spaces. II,”Ukr. Geom. Sb., No. 11, 87–95 (1971).
N. S. Sinyukov,Geodesic Mappings of Riemannian Spaces [in Russian], Nauka, Moscow (1979).
N. S. Sinyukov and S. M. Pokas', “Groups of motions of second degree in an associated Riemannian space,” in:Motions in Generalized Spaces [in Russian], Ryazan (1985), pp. 30–36.
A. S. Solodovnikov, “Projective mappings of Riemannian spaaces,”Usp. Mat. Nauk,11, No. 4, 45–116 (1956).
A. E. Tralle, “On the group of isometries of a generalized Riemannian symmetric space,”Mat. Zametki,41, No. 2, 248–256 (1987).
M. A. Ulanovskii, “On conformai mappings of of the Lorentz metric,”Ukr. Geom. Sb., No. 27, 118–120 (1984).
I. A. Undalova, “Properly Riemannian spaces that admit a stationary-static group of motions,” Published byIzv. Vuzov. Mat., Kazan (1977).
I. A. Undalova, “One-parameter groups of motions with isotropic trajectories,” in:Differentsial'nye i Integral'nye Uravneniya, Gor'kii (1986), pp. 58–62.
I. A. Undalova,One-parameter groups of projective mappings of a Riemannian space with isotropic trajectories [in Russian], Gor'kii University (1986).
I. A. Undalova and S. N. Aryasova, “A pseudo-Riemannian spaceV 4 admitting a one-parameter group of motions with an isolated fixed point” [in Russian], Gor'kii University (1987).
I. A. Undalova and G. R. Eranova, “One-parameter groups of homotheties of a Riemannian space,”Sb. St. Gor'kov. Univ. (Gor'kii Univ. Rpts.), No. 2, 105–109 (1975).
I. A. Undalova and V. N. Markova, “Properly Riemannian spaces admitting groups of motions of type B,”Proc. 8th Sci. Conf. Young Scholars Mech./Math. Fac. Gor'kii Univ., 25–26 April 1983, Part 1, Gor'kii University (1983), pp. 114–118.
I. A. Undalova and L. Yu. Osipova, “One-parameter groups of motions of type B of the Riemannian spacesV 3 andV 4,”Proc. 6th Sci. Conf. Young Scholars Mech./Math. Fac. Gor'kii Univ., Part 3, Gor'kii University (1981), pp. 392–400.
I. A. Undalova and I. V. Tomarova, “A Pseudo-Riemannian spaceV 4 that admits a Killing field with singularity” [in Russian], Gor'kii University (1988).
A. S. Ferzaliev, “On groups of motions in spaces with curvature tensor regarded as a cogredient function of a metric tensor and a skew-symmetric tensor,” in:Probl. Theory Grav. Elem. Part, [in Russian], Atomizdat, Moscow (1970), pp. 137–149.
R. B. Chinak, “On compact groups of isometries conjugate to a subgroup of the orthogonal group,”Sib. Mat. Zh.,28, No. 4, 207–209 (1987).
A. P. Chupakhin, “Nonlinear conformally invariant equations in spacesV 4 with nontrivial conformai group,” in:Solid State Dynamics [in Russian], No. 25, 122–132 (1976).
A. P. Chupakhin, “Nontrivial conformai groups in Riemannian spaces,”Dokl. Akad. Nauk SSSR,246, No. 5, 1056–1058 (1979).
Kh. Shadyev, “On infinitesimal homotheties in the tangent bundle of a Riemannian manifold,”Izv. Vuzov. Mat., No. 9, 77–79 (1984).
Kh. Shadyev, “On infinitesimal homotheties in the tangent bundle of a Riemannian manifold,” in:Probl. Multi-dim. Diff. Geom. and Appl. [in Russian], Samarkand (1988), pp. 12–26.
I. G. Shandra, “Infinitesimal homothetic mappings in the cotangent bundle,”Proc. Sci. Conf. Young Scholars Odessa Univ., May 16–17, 1985, Odessa University (1985), pp. 152–164.
A. P. Shirokov, “The geometry of tangent bundles and spaces over algebras,”Itogi Nauki i Tekhniki, Ser. Probl. Geom.,12, 61–95 (1980).
P. I. Shushpanov, “The group of motions of a spherical space and Lorentz transformations,”Nauch. Tr. Mosk. Inst. Nar. Khoz. (Proceedings of the Moscow Economics Institute), No. 96, 150–177 (1970).
Noill H. Ackerman and C. C. Hsiung, “Isometry of Riemannian manifolds to spheres. II,”Can. J. Math.,28, No. 1, 63–72 (1976).
Lynn L. Ackler and Chuan-Chih Hsiung, “Isometry of Riemannian manifolds to spheres,”Ann. Math. Pura ed Appl,99, 53–64 (1974).
Hassan Akbar-Zadeh and Raymond Couty, “Espaces à tenseur de Ricci parallèle admettant des transformations projectives,”C. R. Acad. Sci.,284, No. 15, A891-A893 (1977).
Hassan Akbar-Zadeh and Raymond Couty, “Espaces à tenseur de Ricci parallèle admettant des transformations projectives,”Rend. Math.,11, No. 1, 85–96 (1978).
Hassan Akbar-Zadeh and Raymond Couty, “Transformations projectives de certaines variétés à connexion métrique,”C. R. Acad. Sci., Sér. 1,298, No. 7, 153–156 (1984).
Hassan Akbar-Zadeh and Raymond Couty, “Transformations projectives des variétés munies d'une connexion métrique,”Ann. Math. Pura ed Appl, No. 148, 251–275 (1987).
A. V. Aminova, “The groups of symmetries in the spaces of general relativity,”Group-theoretic Methods in Mechanics. Proc. Int. Symp. Novosibirsk (1978), pp. 24–33.
A. V. Aminova, “On skew-orthonormal frame and parallel symmetric bilinear form on Riemannian manifolds,”Tensor,45, 1–13 (1987).
A. V. Aminova, “On geodesic mappings of Riemannian spaces,”Tensor,46, 179–186 (1987).
Krishna Amur and S. S. Pujar, “Isometry to spheres of Riemannian manifolds admitting a conformai transformation group,”J. Diff. Geom.,12, No. 2, 247–252 (1977).
Giuseppe Arcidiacono, “A new projective relativity based on the De Sitter universe,”General Relativity and Gravitation,7, No. 11, 885–889 (1976).
Abhay Ashtekar and Anne Magnon-Ashtekar, “A technique for analyzing the structure of isometrics,”J. Math. Phys.,19, No. 7, 1567–1572 (1978).
Abhay Ashtekar and B. G. Schmidt, “Null infinity and Killing fields,”J. Math. Phys.,21, No. 4, 862–867 (1980).
Abhay Ashtekar and Basilis C. Xanthopoulos, “Isometries compatible with aysmptotic flatness at null infinity: a complete description,”J. Math. Phys.,19, No. 10, 2216–2222 (1978).
Daniel Asimov, “Finite groups as isometry groups,”Trans. Amer. Math. Soc.,216, 389–391 (1976).
L. Aulestia, L. Nuñez, A. Patiño, H. Rago, and L. Herrera, “RadiatingC metric: an example of a proper Ricci collineation,”Nuovo dm.,B80, No. 1, 133–142 (1984).
Christiane Barbance, “Transformations conformes des variétés lorentziennes homogènes,”Tensor,39, Commem. Vol. 3, 173–178 (1982).
Christiane Barbance and Yvan Kerbrat, “Sur les transformations conformes des variétés d'Einstein,”C. R. Acad. Sci.,AB286, No. 8, 391–394 (1978).
A. O. Barut, “External (kinematical) and internal (dynamical) conformai symmetry and discrete mass spectrum,” in:Group Theory and Non-Linear Problems, Dordrecht, Boston (1974), pp. 249–259.
André Batbedat, “Sur la conjecture de A. Lichnerowicz,”Pubis. Dép. Math.,11, No. 3, 51–57 (1974).
J. Becker, J. Harnad, M. Perroud, and P. Winternitz, “Tensor fields invariant under subgroups of the conformai group of space-time,”J. Math. Phys.,19, No. 10, 2126–2153 (1978).
M. L. Bedran and B. Lesche, “An example of affine collineation in the Robertson-Walker metric,”J. Math. Phys.,27, No. 9, 2360–2361 (1986).
J. K. Beem, P. E. Ehrlich, and S. Markvorsen, “Timelike isometrics of space-times with nonnegative sectional curvature,” in:Topics in Differential Geometry: Colloq. Debrecen, 26 Aug.–1 Sept. 1984, Vol. 1, Amsterdam (1988), pp. 153–165.
J. K. Beem, P. E. Ehrlich, and S. Markvorsen, “Timelike isometries and Killing fields,”Geom. dedic.,26, No. 3, 247–258 (1988).
Beverly K. Berger, “Homothetic and conformai motions in spacelike slices of solutions of Einstein's equations,”J. Math. Phys.,17, No. 7, 1268–1273 (1976).
David E. Blair, “On the zeros of a conformai vector field,”Nagoya Math. J.,55, 1–3 (1974).
Ashfaque H. Bokhari and Asghar Qadir, “Symmetries of static, spherically symmetric space-times,”J. Math. Phys.,28, No. 5, 1019–1022 (1987).
C. Bona, “Invariant conformai vectors in space-times admitting a groupG 3 of motions acting on spacelike orbitsS 2,”J. Math. Phys.,29, No. 11, 2462–2464 (1988).
Miloš Božek, “Existence of generalised symmetric Riemannian spaces with solvable isometry group,”Čas. pestov. mat.,105, No. 4, 368–384 (1980).
C. P. Boyer and J. D. Finley III, “Killing vectors in self-dual Euclidean Einstein spaces,”J. Math. Phys.,23, No. 6, 1126–1130 (1982).
Thomas P. Branson, “Quasi-invariance of the Yang-Mills equations under conformai transformations and conformai vector fields,”J. Diff. Geom.,16, No. 2, 195–203 (1981).
Frederick Brickell and Kentaro Yano, “Concurrent vector fields and Minkowski structures,”Kodai Math. Semin. Repts.,26, No. 1, 22–28 (1974).
A. J. Briginshaw, “Causality and the group structure of space-time,”Int. J. Theor. Phys.,19, No. 5, 329–345 (1980).
Marek Brodzki and Waclaw Sonelski, “Zastosowanie pewnych podgrup grupy afinicznej zespolonej w geometrycznej teorii seci electrycznych,”Zesz. nauk. Psl., No. 593, 3–15 (1979).
Jochen Brüning and Ernst Heintze, “Représentations des groupes d'isométries dan les sous-espaces propres du laplacien,”C. R. Acad. Sci.,286, No. 20 A221-A223 (1978).
Robert L. Bryant, “Metrics with holonomyG 2 or Spin(7),”Lect. Notes Math., No. 1111, 269–277 (1985).
Robert L. Bryant, “Metrics with exceptional holonomy,”Ann. Math.,126, No. 3, 525–576 (1987).
G. Burdet, J. Patera, M. Perrin, and P. Winternitz, “The optical group and its subgroups,”J. Math. Phys.,19, No. 8, 1758–1780 (1978).
W. Byers, “Isometry groups of manifolds of negative curvature,”Proc. Amer. Math. Soc.,54, 281–285 (1976).
M. Cahen, “A propos du groupe conforme de l'espace de Minkowski,”Bull. Cl. Sci. Acad. Roy. Belg.,62, No. 3, 199–206 (1976).
M. Cahen and Yvan Kerbrat, “Transformations conformes des espaces symétriques pseudo-riemanniens,”C. R. Acad. Sci.,A285, No. 5,B285, No. 5, A383-A385 (1977).
M. Cahen and Yvan Kerbrat, “Champs de vecteurs conformes et transformations conformes des espaces lorentziens symétriques,”J. math, pures et appl.,57, No. 2, 99–112 (1978).
M. Cahen and Yvan Kerbrat, “Transformations conformes des espaces symétriques pseudo-riemanniens,”Ann. math, pura ed appl., No. 122, 257–289 (1982).
Oscar A. Càmpoli, “Clifford isometries of compact homogeneous Riemannian manifolds,”Rev. Union mat. argent.,31, No. 1–2, 44–49 (1983).
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Translated fromItogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 22, 1990, pp. 97–165.
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Aminova, A.V. Groups of transformations of Riemannian manifolds. J Math Sci 55, 1996–2041 (1991). https://doi.org/10.1007/BF01095673
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DOI: https://doi.org/10.1007/BF01095673