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1992 | 63 | 1 | 21-39
Tytuł artykułu

Certain curvature characterizations of affine hypersurfaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
63
Numer
1
Strony
21-39
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-06-13
Twórcy
  • Department of Mathematics, Agricultural University of Wrocław, Norwida 25, 50-375 Wrocław, Poland
Bibliografia
  • [1] N. Bokan, K. Nomizu and U. Simon, Affine hypersurfaces with parallel cubic forms, Tôhoku Math. J. 42 (1990), 101-108.
  • [2] F. Defever and R. Deszcz, On warped product manifolds satisfying a certain curvature condition, Atti Acad. Peloritana Cl. Sci. Fis. Mat. Natur., in print.
  • [3] J. Deprez, R. Deszcz and L. Verstraelen, Pseudosymmetry curvature conditions on hypersurfaces of Euclidean spaces and on Kählerian manifolds, Ann. Fac. Sci. Toulouse 9 (1988), 183-192.
  • [4] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65.
  • [5] R. Deszcz, Notes on totally umbilical submanifolds, in: Geometry and Topology of Submanifolds, Proc. Luminy, May 1987, World Sci., Singapore 1989, 89-97.
  • [6] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065.
  • [7] R. Deszcz, Examples of four dimensional Riemannian manifolds satisfying some pseudosymmetry curvature condition, in: Differential Geometry and its Applications, II, Proc. Avignon, May/June 1988, World Sci., Singapore 1990, 134-143.
  • [8] R. Deszcz, On conformally flat Riemannian manifolds satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145.
  • [9] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudosymmetry curvature conditions, Colloq. Math. 62 (1991), 103-120.
  • [10] R. Deszcz, On pseudosymmetric warped product manifolds, J. Geom., to appear.
  • [11] R. Deszcz, On pseudosymmetric totally umbilical submanifolds of Riemannian manifolds admitting some types of generalized curvature tensors, Zeszyty Nauk. Politech. Śląsk., in print.
  • [12] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 19 (1987), 271-282.
  • [13] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92.
  • [14] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268.
  • [15] R. Deszcz and M. Hotloś, On geodesic mappings in pseudosymmetric manifolds, Bull. Inst. Math. Acad. Sinica 16 (1988), 251-262.
  • [16] R. Deszcz and M. Hotloś, Notes on pseudosymmetric manifolds admitting special geodesic mappings, Soochow J. Math. 15 (1989), 19-27.
  • [17] R. Deszcz and M. Hotloś, Remarks on Riemannian manifolds satisfying certain curvature condition imposed on the Ricci tensor, Prace Nauk. Politech. Szczec. 11 (1988), 23-34.
  • [18] R. Deszcz and M. Hotloś, On conformally related four-dimensional pseudosymmetric metrics, Rend. Sem. Fac. Univ. Cagliari 59 (1989), 165-175.
  • [19] R. Deszcz and M. Hotloś, On conformally related pseudosymmetric metrics, ibid., to appear.
  • [20] R. Deszcz, L. Verstraelen and L. Vrancken, On the symmetry of warped product spacetimes, Gen. Rel. Gravit. 23 (1991), 671-681.
  • [21] K. Nomizu, On the decomposition of generalized curvature tensor fields, in: Differential Geometry in honor of K. Yano, Kinokuniya, Tokyo 1972, 335-345.
  • [22] K. Nomizu, What is affine differential geometry?, in: Proc. Differential Geom., Münster 1982, 42-43.
  • [23] K. Nomizu, Introduction to Affine Differential Geometry, Part I, Lecture Notes, MPI preprint 88-37.
  • [24] K. Nomizu and Ü. Pinkall, On the geometry of affine immersions, Math. Z. 195 (1987), 165-178.
  • [25] Z. Olszak, Bochner flat Kählerian manifolds with certain condition on the Ricci tensor, Simon Stevin 63 (1989), 295-303.
  • [26] B. Opozda, New affine curvature tensor and its properties, lecture given during the meeting 'Current Topics in Affine Differential Geometry', Leuven 1989.
  • [27] B. Opozda and L. Verstraelen, On a new curvature tensor in affine differential geometry, in: Geometry and Topology of Submanifolds, II, Avignon, May/June 1988, World Sci., Singapore 1990, 271-293.
  • [28] U. Simon, Hypersurfaces in equiaffine differential geometry, Geom. Dedicata 17 (1984), 157-168.
  • [29] U. Simon, The fundamental theorem in affine hypersurface theory, ibid. 26 (1988), 125-137.
  • [30] P. Verheyen, Hyperoppervlakken in een affiene ruimte, Ph.D. thesis, Katholieke Universiteit Leuven, 1983.
  • [31] P. Verheyen and L. Verstraelen, Locally symmetric affine hypersurfaces, Proc. Amer. Math. Soc. 93 (1985), 101-105.
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-cmv63i1p21bwm
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