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The scientific heritage of Vasilii Ivanovich Vedernikov

Feb. 11, 1919–March 16, 1991

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List of Publications of V. I. Vedernikov

  1. —, “Conformal covering of surfaces,”Dokl. Akad. Nauk SSSR,73 437–440 (1950).

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  2. —, “Conformal covering of surfaces,”Uch. Zapiski Univ.,110, No. 3, 35–55, Kazan, (1950).

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  3. —, “Conformal covering of surfaces with preservation of conjugate geometries,”Tr. Univ. (Voronezh),33, 37–42, (1954).

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  4. —, “Metric characteristic of the main images and values of the conform surface theory,” (in collaboration with V. A. Tikhonov),Tr. Univ. (Voronezh),33, 43–52, (1954).

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  5. V. I. VEDERNIKOV, “Conformal covering of surfaces,” In:Trudy 3-go Vsesoyuznogo Mat. Sjezda, Vol. 1, Moscow (1956), pp. 144–145.

  6. —, “Surfaces enveloping the family of hyperspheres,”Izv. Vuzov. Mat.,1, 89–97 (1957).

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  7. —, “On a multidimensional generalization of the Dupin cyclide,”Izv. Vuzov. Mat.,6, 58–72 (1958).

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  8. —, “Surfaces of rotation of the Euclidean spaceE n ,”Izv. Vuzov. Mat.,1, 39–47 (1960).

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  9. V. I. VEDERNIKOV, “On the theory of curves of the Euclidean spaceE n ,” In:Trudy 2oj Nauchnoi Konf. Mat. Kafedr Ped. In-tov Povolzk’ya, Vol. 1, Kuibyshev (1962), pp. 136–137.

  10. —, “On the theory of curves of the Euclidean spaceE n ,”Uch. Zap. Ped. Inst. (Gorkii),41, 3–6 (1962).

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  11. —, “Descriptive geometry of the Lobachevskii space” (in collaboration with A. I. Makarova and E. N. Rudenko),Tr. Univ. (Voronezh),61, 3–7 (1962).

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  12. V. I. VEDERNIKOV, “On linear representation of homogeneous spaces,” In:Tr. 2oi Nauch. Konf. Mat. Kafedr Ped. In-tov Povolzhya, Vol. 1, Kuibyshev (1962), pp. 135.

  13. V. I. VEDERNIKOV, “On limiting cycles of differential equation system,” In:Tr. 2oi Nauch. Konf. Mat. Kafedr Ped. In-tov Povolzhya, Vol. 1, Kuibyshev (1962), pp. 137–138.

  14. —, “On regular semi-stable limiting cycles of a system of ordinary differential equations,”Uch. Zapiski Ped. Inst. (Gorkii),41, 35–43 (1962).

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  15. —, “(n−1)-Parametric families of hyperspheres inM n ,”Izv. Vuzov. Mat., No. 2, 7–11 (1962).

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  16. —, “A family of hypershperes of relative zero curvature,”Uch. Zapiski Ped. Inst. (Gorkii),41, 12–19 (1962).

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  17. V. I. VEDERNIKOV, “A family of hypershperes of relative zero curvature,” In:Tr. 2oi Nauch. Konf. Mat. Kafedr Ped. In-tov Povolzhya, Vol. 2, Kuibyshev (1962), pp. 135–136.

  18. V. I. VEDERNIKOV, “A generalization of the A. P. Norden normalization method,” In: IVsesoyuzn. Geom. Konf., Tez. Dokl., Kiev (1962), p. 43.

  19. —, “Conformal covering of surfaces in the spaceM n ,”Izv. Vuzov. Mat., No. 1, 33–41 (1963).

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  20. —, “Metric characteristic of some classes of hypersurfaces,”Izv. Vuzov. Mat., No.4, 26–32 (1963).

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  21. —, “A generalization of A. P. Norden for the case of fibre bundles,”Uch. Zapiski Univ. (Kazan’),123, No. 1, 3–23 (1950).

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  22. —, “Reducible infinitesimal connections,”Mit. Mat. Sb.,3, No. 2, 225 (1963).

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  23. —, “Studies in geometry of the members of mathematical chairs of the Gorkii Pedagogical Institute,”Lit. Mat. Sb.,3 No. 2, 213–215 (1963).

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  24. —, “A method of normalization in the Lie sphere geometry” (in collaboration with V. V. Gorodetskii),Lit. Mat. Sb.,3, No. 2, 232 (1963).

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  25. —, “Pseudolinear connection,”Izv. Vuzov. Mat., No. 2, 41–52 (1964).

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  26. —, “On conjugate connections,”Izv. Vuzov. Mat., No. 4, 19–29 (1964).

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  27. V. I. VEDERNIKOV, “Symmetric homogeneous spaces and their role in the Cartan’s connection theory,” In:Dokl. 3ei Sib. Konf. po Matem. i Mekh., Tomsk (1964), pp. 185–186.

  28. V. I. VEDERNIKOV, “Reductive Cartan connections and their importance for the normalization theory,” In: IIVsesoyuzn. Geom. Konf., Tezisy Dokl., Khar’kov (1964), pp. 41–42.

  29. —, “Conjugate connections in the space of contact elements of a centroaffine space,” (in collaboration with N. N. Chudinov)Volzh. Mat. Sb. (Kuibyshev),2, 15–20 (1964).

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  30. —, “Completely reducible connections,”Izv. Vuzov. Mat., No.1, 33–44 (1965).

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  31. —, “Symmetrical spaces and conjugate connections,”Uch. Zapiski Univ. (Kazan’),125, No. 1, 7–59 (1965).

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  32. V. I. VEDERNIKOV, “Generalized symmetrical pairs,” In:Materialy II Pribalt. Geom. Konf., Tartu (1965), pp. 36–37.

  33. V. I. VEDERNIKOV, “On constructing symmetry images,” In:Materialy II Pribalt. Geom. Konf., Tartu (1965), pp. 37–39.

  34. V. I. VEDERNIKOV, “Conjugate connections as normalized infinitesimal connection,” In:Materialy IIPribalt. Geom. Konf., Tartu (1965), pp. 39–42.

  35. —, “The hypersurfaces of Euclidean space enveloping them-parameteric family of hyperspheres,”Volzh. Mat. Sb. (Kuibyshev),4, 8–13 (1966).

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  36. V. I. VEDERNIKOV, “Pairs of conjugate connections,” In:Tez. Kr. Nauch. Soobshchenii Mezhdunar. Kongressa Matematikov, Sectsiya 9, Moscow (1966), p. 24.

  37. —, “Symmetric spaces. Conjugate connections as normalized connection,” In:Trudy Geometr. Seminara, Vol. 1 All-Union Institute for Scientific Information, Akad. Nauk SSSR, Moscow (1966), pp. 63–88.

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  38. V. I. VEDERNIKOV, “A global definition of conjugate connections,” In:Tezisy Dokladov IIResp. Konf. Matematikov Belorussii, Part I, Minsk (1967), pp. 60–61.

  39. V. I. VEDERNIKOV, “On fibre bundles in homogeneous spaces,” In:Tezisy Dokl. 3ei Pribalt. Geom. Konf., Palanga (1968), pp. 40–41.

  40. V. I. VEDERNIKOV, “Boundary homogeneous spaces,” In:Rezyume Nauch. Soobshchenii IXVsesoyuznogo Algebraicheskogo Kollokviuma, Gomel’ (1968), pp. 45–46.

  41. V. I. VEDERNIKOV, “A generalization of the A. P. Norden normalization method,” In:Tr. II Resp. Konf. Matematikov Belorussii, Minsk (1969), pp. 60–62.

  42. V. I. VEDERNIKOV, “Boundary homogeneous spaces,” In: IVVsesoyuzn. Geom. Konf., Tezisy Dokl., Tbilisi (1969), pp. 38–39.

  43. —, “The normalization method in the Lie sphere geometry” (in collaboration with V. V. Gorodetskii),Uch. Zap. Ped. Inst. (Smolensk),8, 23–30 (1969).

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  44. V. I. VEDERNIKOV, “Equivalence of manifold mappings into a homogeneous space,” In:Tezisy Dokladov 3ei Resp. Konf. Matematikov Belorussii, Part 1, Minsk, (1971).

  45. —, “Infinitesimal pseudoconnections,”Izv. Vuzov. Mat., No. 1, 3–11 (1972).

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  46. V. I. VEDERNIKOV, “ϕ-Structures in the principal G-bundles,” In: VVsesoyuzn. Geom. Konf., Tezisy Dokl., Samarkand, (1972), p. 33.

  47. —, “Delected topics in differential geometry (in collaboration with V. T. Vodnev) [in Russian],Izd-vo Belgosuniversitet Press, Minsk, (1972).

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  48. —, “On one special class of homogeneous spaces,”Izv. Vuzov. Mat., No. 12, 17–22 (1972).

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  49. V. I. VEDERNIKOV, “On manifolds over modules” (in collaboration with I. V. Bel’ko), In:Materialy IV Pribalt. Geom. Konf., Tartu (1973), pp. 20–21.

  50. V. I. VEDERNIKOV “Global net theory” (in collaboration with V. V. Babich), In:Materialy IVPribalt. Geom. Konf., Tartu (1973), pp. 11.

  51. — “ϕ-Structures in principalG-bundles,”Dokl. Akad. Nauk BSSR,17, No. 8, 689–691 (1973).

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  52. — “Affine Weyl connections and connections in linear bundles with homogeneous complex fibres” (in collaboration with L. I. Vedernikova),Izv. Vuzov. Mat., No.5, 47–51 (1974).

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  53. V. I. VEDERNIKOV “ϕ-structures and conjugate connections in principalG-bundles,” In:Trudy Seminara Kaf. Geometrii No. 7, Izd-vo Kazan. Un-ta, Kazan’ (1974), pp. 20–27.

  54. V. I. VEDERNIKOV “Manifolds of lines of a three-dimensional elliptic space,” In:Tezisy Dokl. IVResp. Konf. Matematikov lorussii, Part 2, Minsk (1975), p. 76.

  55. V. I. VEDERNIKOV “Morphisms of symmetric spaces generated by a group of non-Euclidean motions,” (in collaboration with S. V. Vedernikov and T. V. Tsvir), In: VIVsesoyuzn. Geom. Konf. po Sovr. Probl. Geometrii, Tezisy Dokl., Vil’nyus (1975), pp. 50–51.

  56. V. I. VEDERNIKOV “Manifolds of lines of a three-dimensional elliptic space,” In:Trudy Seminara Kafedry Geometrii, No. 8, Izd-vo Kazan. Univ., Kazan’ (1975), pp. 41–48.

  57. V. I. VEDERNIKOV “Domains of symmetric spaces generated by the group SL(2, ℂ),” (in collaboration with S. V. Vedernikov), In:Tezisy Dokl. Vses. Nauch. Konf. po Neevklidovoi Geometrii “150 Let Geometrii Lobachevskogo,” Kazan’ (1976), p. 47.

  58. — “Fubini spheres and their generalizations,”Izv. Vuzov. Mat., No. 6, 14–19 (1976).

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  59. — “Symmetrical spaces and their generalizations,” In:Algebra. Topology. Geometry, Vol. 14,Itogi Nauki i Tekhn., All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1976), pp. 249–280.

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  60. V. I. VEDERNIKOV “On program and content of the course of differential geometry,” (in collaboration with I. V. Bel’ko), In:Tezisy Dokl. i Soobshchenii IIIZonal’nogo Soveshchaniya-Seminara Zav. Kafedramy i Vedushchikh Lektorov Matematiki Vuzov Belorusskoi, Latviiskoi, Litovskoi, Estonskoi SSR i Kaliningradskoi Oblasti RSFSR, Minsk (1977), p. 23.

  61. V. I. VEDERNIKOV “On the course of geometry foundations” (in collaboration with A. A. Burdun), In:Tezisy Dokl. i Soobshchenii IIIZonal’nogo Soveshchaniya-Seminara Zav. Kafedrami i Vedushchikh Lektorov Matematiki Vuzov Belorusskoi, Latviiskoi, Litovskoi, Estonskoi SSR i Kaliningradskoi Oblasti RSFSR, Minsk (1977), pp. 23–24.

  62. V. I. VEDERNIKOV “On spaces with symmetries,” (in collaboration with A. S. Fedenko), In:Vses. Nauch. Konf. po Neevklidovoj Geometrii “150 Let Geometrii Lobachevskogo,” Plenarnye Doklady, Moscow (1977), pp. 42–49.

  63. V. I. VEDERNIKOV “Homogeneous affinor spaces and flat nets in an affine space,” (in collaboration with S. V. Vedernikov), In:Tez. Dokl. VPribaltiiskoi Konf., Druskininkai (1978), p. 19.

  64. —Book of problems in differential geometry (in collaboration with I. V. Bel’ko, V. T. Vodnev, A. A. Gusak, A. I. Nakhimovskaya, A. P. Ryabushko, L. K. Tutaev, and A. S. Fedenko) [in Russian], Nauka, Moscow (1979).

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  65. — “Space of pseudo-frames,”Differentsial’naya Geometriya Mnogoobrasii Figur, No. 10, 16–21 (1979).

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  66. V. I. VEDERNIKOV “Induced invariant connections of associative algebra orbits,” (in collaboration with L. I. Vedernikova), In: VIIVses. Geom. Konf. po Sovr. Probl. Geometrii, Tezisy Dokl., Minsk (1979), p. 40.

  67. V. I. VEDERNIKOV “On belonging conditions,” (in collaboration with L. I. Vedernikova), In:Tezisy Dokl. VResp. Konf. Matematikov Belorussii, Part 1, Grodno (1980), pp. 32–33.

  68. V. I. VEDERNIKOV “Geometries of transformation groups,” (in collaboration with L. I. Vedernikova), In:Tezisy Dokl. XVIVses. Algebr. Konf., Part I, Leningrad (1981), p. 31.

  69. —Problemas de geometria diferencial (in collaboration with I. V. Bel’ko, V. T. Vodnev, A. A. Gusak, A. I. Nakhimovskaya, A. P. Ryabushko, L. K. Tutaev, and A. S. Fedenko) Mir, Moscow (1981).

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  70. V. I. VEDERNIKOV “Geometric studies in Byelorussia,” (in collaboration with A. S. Fedenko), In:Aktual’nye Problemy Obshchestvennykh Nauk. Aktual’nye Problemy Estestvennykh Nauk, Tez. Dokl., Minsk (1982), p. 81.

  71. —Differential Geometry (in collaboration with I. V. Bel’ko, A. A. Burdun, and A. S. Fedenko), BGU Press, Minsk (1981).

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  72. —Recueil d’exercices de géométrie differentielle (in collaboration with I. V. Bel’ko, V. T. Vodnev, A. A. Gusak, A. I. Nakhimovskaya, A. P. Ryabushko, L. K. Tutaev, and A. S. Fedenko) Mir, Moscow (1982).

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  73. V. I. VEDERNIKOV “On teaching differential geometry at universities” (in collaboration with V. V. Balashchenko and S. V. Vedernikov), In:Tezisy Dokl. VZonal’nogo Soveshchaniya-Seminara Zav. Kafedrami i Vedushchikh Lektorov Matematiki Vuzov Belorusskoi, Latviiskoi, Litovskoi, Estonskoi SSR i Kaliningradskoi Oblasti RSFSR, Vilnius (1983), pp. 41–42.

  74. V. I. VEDERNIKOV “Geometry of homogeneous spaces generated by motion groups of quasi-non-Euclidean spaces,” (in collaboration with L. I. Vedernikova), In:Tez. Dokl. VIPribalt. Geom. Konf., Tallinn (1984), p. 27.

  75. V. I. VEDERNIKOV “Geometry of the homogenous space of positive definite Hermitian forms,” (in collaboration with S. V. Vedernikov), In: VIIVses. Geom. Konf. po Sovr. Probl. Geometrii, Tezisy Dokl., Odessa (1984), p. 28.

  76. — “Homogeneous space of central quadrics of an affine space” (in collaboration with S. V. Vedernikov),Izv. Vuzov. Mat., No. 7, 34–38 (1984).

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  77. V. I. VEDERNIKOV “On forms of teaching mathematicians at universities,” (in collaboration with V. V. Balashchenko), In:Tezisy Dokl. VIZonal’nogo Soveshchaniya-Seminara Zav. Kafedrami i Vedushchikh Lektorov Matematiki Vuzov Belorusskoi, Latviiskoi, Litovskoi, Estonskoi SSR i Kaliningradskoi Oblasti RSFSR, Part II, Tallin (1987), pp. 20–21.

  78. — “60 years of A. A. Gusak” (in collaboration with N. V. Metel’skii and A. S. Fedenko),Metematika Shkole, No. 5, 72–73 (1987).

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  79. — “Geometry of homogeneous spaces generated byG-space morphisms,” (in collaboration with S. V. Vedernikov), In:Problemy Geometrii, Vol. 19,Itogi Nauki i Tekhn., All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1987), pp. 155–185.

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  80. V. I. VEDERNIKOV “Geometry generated by the endomorphisms of the affine transformation group,” In:Tezisy Soobshch. XVses. Geom. Konf., Kish’inev (1988), p. 60.

  81. V. I. VEDERNIKOV “60 years of A. S. Fedenko,” (in collaboration with A. A. Gusak and A. K. Lapkovskii),Matematika Shkole, No. 4, 123–124.

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Authors
  1. V. V. Balashchenko
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  2. S. V. Vedernikov
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  3. N. A. Stepanov
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  4. A. S. Fedenko
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 8, Geometriya-1, 1993.

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Balashchenko, V.V., Vedernikov, S.V., Stepanov, N.A. et al. The scientific heritage of Vasilii Ivanovich Vedernikov. J Math Sci 74, 961–976 (1995). https://doi.org/10.1007/BF02362829

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