REFERENCES
V. N. Abdullin, "n-Dimensional Riemannian spaces admitting fields of covariantly constant symmetrical tensors of general form, I, II," Izv. Vuzov, Mat., No. 5, 3-13 (1970); No. 6, 13-15 (1070).
D. Alekseevsky and S. Marchiafava, "Quaternionic-like structures on a manifold, I. 1-Integrability and the integrability condition," Rend. Linc. Mat. Appl., 4, No. 1, 443-452 (1993).
B. V. Balachshenko and N. A. Stepanov, "Canonical affinor structures of the classical type on regular ?-spaces," Mat. Sb., 186, No. 1, 3-34 (1995).
A. V. Boyarinova, "On the space of essential infinitesimal transformations," Izv. Vuzov, Mat., No. 8, 3-12 (1997).
A. Carfagna D'Andrea and R. Di Febo Marinelli, "Su una generalizzazione delle strutture quasi tangenti," Rend. Math. Appl., 2, No. 2, 257-267 (1982).
N. G. Chebotarev, Introduction to the Theory of Algebras [in Russian], Moscow-Leningrad (1949).
_ E. S. Clark and D. S. Goel, "Almost tangent manifolds of secondo order," Tohoku Math. J., 24, No. 1, 79-92 (1972).
C. Curtis andI. Rainer, Representation Theory of Finite Groups and Associative Algebras [Russian translation], Moscow (1969).
S. Das Lovejoy, "F-Structure manifoldw ith some linear connections," Rocz. PTM, Ser. 1, 32, 19-27 (1992).
S. Das Lovejoy, "On a structure satisfying F k + (-1)k+1 F = 0," Int. J. Math. Math. Sci., 19, No. 1, 125-130 (1996).
S. Das Lovejoy, "Manifoldw ith the structure satisfying F k+1–a 2 F k-1 = 0," Mathematica, 37, Nos. 1-2, 81-91 (1995).
M. De León, I. Méndez, and M. Salgado, "p-Almost tangent structures," Rend. Circ. Math. Palermo, 37, No. 2, 282-294 (1988).
K. Deszyński, "Notes on polynomial structures equipped with a Lorentzian metric," Zesz. Nauk. UJ, Acta Math., No. 28, 11-18 (1991).
B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry. Methods and Applications [in Russian], Nauka, Moscow (1986).
H. A. Eliopoulos, "Structures r-tangentes sur les variétés différentiables," C. R. Acad. Sci., 263, No. 13, A413-A416 (1966).
H. A. Eliopoulos, "On certain Riemannian structures compatible with r-tangent structures," Tensor, 39, 23-30 (1982).
F. Etayo, "On the horizontal lift of a connection to the tangent bundle," Atti Semin. Mat. Fis. Univ. Modena, 43, No. 2, 505-510 (1995).
G. D. Fattaev, "On a certain almost holomorphic tensor field in a manifoldan dits pure affinor subbundle," Preprint, Kazan Univ., Kazan (1992).
G. D. Fattaev, "Horizontal lift of tensor fields to a pure a.nor subbundle," Preprint, Kazan Univ., Kazan (1992).
M. Fernandez and A. Alcaraz, "Polynomial structures of kind (h, k)," Bull. Math. Soc. Sci. Math. RSR, 30, No. 4, 295-299 (1986).
L. Filippova, "The tangent bundles like a B-manifold," In: Proc. Inst. Lect. Short Commun. Deliv. 5th Int. Colloq. Differ. Equat., Plovdiv, Aug. 18-23 (1994), Plovdiv (1994), p. 60.
L. Filippova, "Integrable strongly degenerate semi-tangent structure," J. Tech. Univ. Plovdiv, 2, 89-94 (1996).
S. Gaforov, "Lie derivative and horizontal lift to a semi-tangent bundle of the first order," Preprint, Kazan (1991).
S. Gaforov, "A semi-tangent bundle of a two-dimensional manifold and its plural interpretation," Preprint, Kazan Univ., Kazan (1992).
S. Gaforov, "On one example of a semi-tangent bundle of the second order," Preprint, Kazan Univ., Kazan (1992).
S. Gaforov, "Holomorphic-geodesic transformations in a semi-tangent bundle of a higher order," Preprint, Kazan Univ., Kazan (1992).
S. Gaforov, "Lie derivative in a semi-tangent bundle of the second order," Preprint, Kazan Univ., Kazan (1992).
S. Gaforov, "Lie derivative in semi-tangent bundles," In: Tr. Geom. Sem. [in Russian], Vol. 22, Kazan (1994), pp. 5-11.
J. Gancarzewicz and S. Mahi, "Lifts of 1-forms to a tangent bundle of higher order," Czech. Math. J., 40, No. 3, 397-407 (1990).
F. R. Gantmakher, Matrix Theory [in Russian], Moscow (1966).
B. A. Gaukhman, "On diagonazable almost tensor structures," Usp. Mat. Nauk, 19, No. 6, 226-228 (1964).
S. L. Goldberg and K. Yano, "Polynomial structures on manifolds," Kodai Math. Semin. Repts., 22, No. 2, 199-218 (1970).
K. I. Gribachev, G. D. Dzhelepov, and D. G. Mekerov, "On the geometry of almost B-manifolds," Dokl. Bolg. Akad. Nauk, No. 5, 563-565 (1985).
V. G. Gupta and C. P. Awasthi, "Integrability conditions of an F(k, k-2)-structure satisfying F k + F k-2 = 0 (k is odd)," Publ. Math., 34, 251-257 (1987).
T. Hangan, "On the canonical form of a second order mixed tensor," Rev. Math. Pure Appl., 7, No. 4, 617-626 (1962).
T. Hangan, "Sur intégrabilité de certaines G-structures tensorielles," C. R. Acad. Sci., A288, No. 17, A835-A837 (1979).
T. V. Kirsanova, "Semi-tangent structures of the first order," In: Tr. Geom. Sem. [in Russian], Vol. 16, Kazan (1984), pp. 41-46.
T. V. Kirsanova, "Lifts andcon nections on a manifold with semi-tangent structure," In: Differential Geometry. Structures on Manifolds and Their Applications [in Russian], Vol. 8, Saratov (1985), pp. 36-44.
I. Kolarz, "Natural bundles and operators," In: Progress in Science and Technology, Series on Problems of Geometry [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1991), pp. 67-98.
I. ř and J. Slovák, "Prolongation of vector fields to jet bundles," Rend. Circ. Mat. Palermo, Ser. 2, 39, No. 2, 103-111 (1990).
G. I. Kruchkovich, "Integrability conditions of a regular hypercomplex structure on a manifold," Ukr. Geom. Sb., No. 9, 67-75 (1970).
G. I. Kruchkovich, "Hypercomplex structures on a manifolds, I," Tr. Sem. Vect. Tens. Anal., 16, 174-201 (1972).
J. Lehmann-Lejeune, "Intégrabilité des G-structures définies par une 1-forme 0-deformable à valèurs dans le fibre tangent," Ann. Inst. Fourier, 16, No. 2, 329-387 (1966-1967).
L. B. Lobanova, "Geometries over polynomial algebras," Geom. Sb. (Tomsk), 24, 104-106 (1984).
M. A. Malakhal'tsev, "On a certain class of manifolds over the algebra of dual numbers," In: Tr. Geom. Sem. [in Russian], Vol. 21, Kazan (1991), pp. 70-79.
G. A. Mazanova, "On the structure of representations of a certain non-Frobenius algebra," Preprint Bashk. Gos. Ped. Inst., Ufa (1987).
G. A. Mazanova, "On the module of the r-regular representation of a certain non-Frobenius algebra," In: Proc. Intern. Sci. Conf., Kazan, Aug. 18-22 (1992) [in Russian], Part I, Kazan (1992), p. 53.
R. Miron and G. Atanasiu, "Differential geometry of the K-osculator bundle," Rev. Roum. Math. Pure Appl., 41, Nos. 3-4, 205-236 (1996).
T. G. Nakov, "On certain metric connections with binary affinor structure," Nauchni Trodove, Plovdiv Univ., Vol. 11, Book 2, 9-17 (1973).
J. Nikič, "On integrability conditions of an f(2k + 1,-1)-structure," In: Differ. Geom. and Its Appl.: Proc. Conf., Dubrovnik, June 26-July 3 (1988), Fac. Math. Univ. Beograd, Inst. Math. Univ., Novi Sad, Novi Sad (1989), pp. 253-265.
A. P. Norden, "On a certain class of four-dimensional A-spaces," Izv. Vuzov, Mat., No. 4, 145-157 (1960).
A. P. Norden, "Spaces of Cartesian composition," Izv. Vuzov, Mat., No. 4, 117-128 (1963).
A. P. Norden, "Composition theory," In: Progress in Science and Technology, Series on Problems in Geometry [in Russian], Vol. 10, All-Union Institute for Scientific andT echnical Information (VINITI), Akad. Nauk SSSR, Moscow (1978), pp. 117-146.
N. M. Ostianu, "Step-like fibereds paces," In: Tr. Geom. Sem. [in Russian], Vol. 5, VINITI, Moscow (1974), pp. 259-309.
T. A. Panteleeva, "Lifts of double projectable tensor fields to a semi-tangent bundle of the second order," Preprint, Kazan Univ., Kazan (1985).
T. A. Panteleeva, "Holomorphic-geodesic transformations in a semi-tangent bundle of the second order," Preprint, Kazan Univ., Kazan (1986).
T. A. Panteleva, "Holomorphically-geodesic flat spaces," In: Tr. Geom. Sem. [in Russian], Vol. 19, Kazan (1989) pp. 91-97.
T. A. Panteleeva, "On a certain class of semi-tangent structures of the second order," In: Intern. Sci. Conf., Kazan, Aug. 18-22 (1992) [in Russian], Part 1, Kazan (1992), p. 72.
T. A. Panteleeva, "Double projectable tensor fields and connections in a semi-tangent bundle of the second order," In: Tr. Geom. Sem. [in Russian], Vol. 17, Kazan (1996), pp. 43-53.
E. V. Pavlov, "A certain class of spaces with dual structure," Nauchni Trodove, Plovdiv Univ., Vol. 11, Book 3, 17-23 (1973).
E. V. Pavlov, "Some connections in a manifolde quipped with an irregular dual structure," Nauchni Trudove, Plovdiv Univ., Vol. 11, Book 4, 145-155 (1973).
E. V. Pavlov, "Conformally equivalent generalized B-manifolds," Dokl. Bolg. Akad. Nauk, 35, No. 2, 141-144 (1982).
E. V. Pavlov and H. T. Hopteriev, "Conformally equivalent B-manifolds," Dokl. Bolg. Akad. Nauk, 39, No. 1, 15-17 (1986).
S. L. Pevzner, "Automorphisms of quadrics in a non-Euclidean space that are represented by motions of plural non-Euclidean space," Izv. Vuzov, Mat., No. 9, 69-77 (1968).
M. O. Rakhula, "Infinitesimal connection in a bundle," In: Progress in Science and Technology, Series on Problems in Geometry [in Russian], Vol. 8, All-Union Institute for Scientific andTechnical Information (VINITI), Akad. Nauk SSSR, Moscow (1977), pp. 163-182.
M. O. Rakhula, "Catastrophe theory and differential geometry," In: Progress in Science and Technology, Series on Problems in Geometry [in Russian], Vol. 16, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1984), pp. 35-80.
A. A. Salimov, "A note on almost integrability of a structure," Izv. Vuzov, Mat., No. 12, 70-71 (1985).
A. A. Salimov, "Almost integrability of a multia.ne structure," Izv. Vuzov, Mat., No. 6, 78-80 (1988).
A. A. Salimov, "Almost ?-holomorphic tensors and their properties," Dokl. Rossiisk. Akad. Nauk, 324, No. 3, 533-536 (1992).
A. A. Salimov, "A new method in the lift theory of tensor fields to the tensor bundle," Izv. Vuzov, Mat., No. 3, 69-85 (1994).
A. A. Salimov, "Complete lifts of tensor fields to a pure tensor subbundle," In: Tr. Geom. Sem. [in Russian], Vol. 22, Kazan (1994), pp. 69-78.
G. Scheffers, "Verallgemeinerung der Grundlagen der gewöhnlich complexen Funktionen," Berichte Sächs. Akad. Wiss., 45, 828-848 (1983).
B. N. Shapukov, "Connections on di.erentiable bundles," In: Progress in Science and Technology, Series on Problem in Geometry [in Russian], Vol. 15, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1983), pp. 61-93.
A. P. Shirokov, "On a certain property of covariantly constant affinors," Dokl. Akad. Nauk SSSR, 102, No. 3, 461-464 (1955).
A. P. Shirokov, "Structures on differentiable manifolds," In: Progress in Science and Technology, Series on Algebra, Topology, and Geometry [in Russian], Vol. 11, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1974), pp. 153-207.
V. V. Shurygin, "Manifolds over algebras and their application in geometry of jet bundles," Usp. Mat. Nauk, 48, No. 2, 75-106 (1993).
V. V. Shurygin, "Manifolds over local algebras that are equivalent to jet bundles," Izv. Vuzov, Mat., No. 10, 68-79 (1992).
N. Soare, "Sur quelques f-connexions linéaires," Kiv. Mat. Univ. Parma, No. 14, 143-150 (1988).
D. A. Suprunenko and R. I. Tyshkevich, Commuting Matrices [in Russian], Minsk (1966).
S. Tachibana and S. Koto, "On almost-analytic functions, tensors, and invariant subspaces," Tohoku Math. J., 14, No. 2, 177-186 (1962).
M. M. Tsalenko, "Integrability of a tensor structure on a manifoldof class C ?," In: Tr. Geom. Sem. [in Russian], Vol. 2, VINITI (1969), pp. 333-355.
F.-J. Turiel, "Classification locale des tenseurs de type (1, 1) presque plats," C. R. Acad. Sci., Sér. 1, 319, No. 5, 471-474 (1994).
J. Vanžura, "Simultaneous integrability of an almost tangent structure and a distribution," Demonstr. Math., 19, No. 2, 359-370 (1980).
J. Vanžura and A. Vanžurova, "Polynomial mappings of polynomial structures with simple roots," Acta Univ. Palack. Olomouc, Fac. Rerum Natur. Math., 114, No. 33, 157-164 (1997).
A. Vanžurova, "Double linear conections," Acta Univ. Palack. Olomouc, Fac. Rerum Natur. Math., 100, No. 30, 275-271 (1991).
T. B. Vasil'kina, "Horizontal lifts of tensor fields andcon nections on a manifoldw ith semi-tangent structure," Preprint, Mordovskii Univ., Saransk (1990).
T. B. Vasil'kina, "Holomorphic-projective transformations of a connection and in variant objects on a manifoldw ith semi-tangent structure," Preprint, Mordovskii Univ., Saransk, (1994).
M. K. Vassileva, " Generalized B-manifolds with bounded holomorphic 4-curvature," Serdika, Bolg. Mat. Spis., 13, No. 4, 375-378 (1987).
V. V. Vishnevskii, "Structures of projective spaces generatedb y affinors," Izv. Vuzov, Mat., No. 6, 35-46 (1969).
V. V. Vishnevskii, "Affinor structures of affine connection spaces," Izv. Vuzov, Mat., No. 1, 12-23 (1970).
V. V. Vishnevskii, "Polynomial algebras anda. nor structures," In: Tr. Geom. Sem. [in Russian], Vol. VI, Kazan (1971), pp. 22-35.
V. V. Vishnevskii, "An example of an irregular semi-tangent structure," In: Geometry of Generalized Spaces [in Russian], Ufa (1983), pp. 26-32.
V. V. Vishnevskii, "On a geometric model of semi-tangent structures," Izv. Vuzov, Mat., No. 3, 32-34 (1983).
V. V. Vishnevskii, "Manifolds over algebras of plural numbers and semi-tangent structures," In: Progress in Science and Technology, Series on Problems of Geometry [in Russian], Vol. 20, All-Union Institute of Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1988), pp. 35-74.
V. V. Vishnevskii, "Semi-tangent bundles and local algebras," In: Dedicated to the Memory of N. I. Lobachevskii [in Russian], Vol. 2, Kazan Univ., Kazan (1992), pp. 3-8.
V. V. Vishnevsky, "On semi-tangent fibre bundle of higher order," In: Proc. Int. Sci. Conf., Kazan, Aug. 18-22 (1992), Part 1, Kazan (1992), pp. 127-128.
V. V. Vishnevskii, "Lifts of differential-geometric objects to semi-tangent bundles of higher order," Izv. Vuzov, Mat., No. 5, 16-24 (1995).
V. V. Vishnevskii, "A manifoldw ith a pair of commutative semi-tangent structures," Izv. Vuzov, Mat., No. 6, 1-8 (1998).
V. V. Vishnevskii and S. Gaforov, "Semi-tangent bundles of higher order and the Lie differentiation," Vestn. Pedagog. Univ., Ser. Estestv. Nauk (Dushanbe), No. 4, 1-13 (1986).
V. V. Vishnevskii and T. A. Panteleeva, "Holomorphic prolongation of objects to a semi-tangent bundle of the second order," Izv. Vuzov, Mat., No. 9, 3-10 (1985).
V. V. Vishnevskii, A. P. Shirokov, and V. V. Shurygin, Spaces over Algebras [in Russian], Kazan Univ., Kazan (1985).
Rights and permissions
About this article
Cite this article
Vishnevskii, V.V. Integrable Affinor Structures and Their Plural Interpretations. Journal of Mathematical Sciences 108, 151–187 (2002). https://doi.org/10.1023/A:1012818202573
Issue Date:
DOI: https://doi.org/10.1023/A:1012818202573