@article{bwmeta1.element.bwnjournal-article-cmv63i1p21bwm, author = {Ryszard Deszcz}, title = {Certain curvature characterizations of affine hypersurfaces}, journal = {Colloquium Mathematicae}, volume = {63}, year = {1992}, pages = {21-39}, zbl = {0797.53005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv63i1p21bwm} }
Deszcz, Ryszard. Certain curvature characterizations of affine hypersurfaces. Colloquium Mathematicae, Tome 63 (1992) pp. 21-39. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv63i1p21bwm/
[000] [1] N. Bokan, K. Nomizu and U. Simon, Affine hypersurfaces with parallel cubic forms, Tôhoku Math. J. 42 (1990), 101-108. | Zbl 0696.53006
[001] [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. | Zbl 0780.53017
[002] [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. | Zbl 0668.53010
[003] [4] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. | Zbl 0678.53022
[004] [5] R. Deszcz, Notes on totally umbilical submanifolds, in: Geometry and Topology of Submanifolds, Proc. Luminy, May 1987, World Sci., Singapore 1989, 89-97. | Zbl 0735.53042
[005] [6] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. | Zbl 0707.53020
[006] [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.
[007] [8] R. Deszcz, On conformally flat Riemannian manifolds satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145. | Zbl 0742.53006
[008] [9] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudosymmetry curvature conditions, Colloq. Math. 62 (1991), 103-120. | Zbl 0738.53008
[009] [10] R. Deszcz, On pseudosymmetric warped product manifolds, J. Geom., to appear. | Zbl 0843.53011
[010] [11] R. Deszcz, On pseudosymmetric totally umbilical submanifolds of Riemannian manifolds admitting some types of generalized curvature tensors, Zeszyty Nauk. Politech. Śląsk., in print.
[011] [12] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 19 (1987), 271-282. | Zbl 0633.53031
[012] [13] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92. | Zbl 0698.53011
[013] [14] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268. | Zbl 0707.53019
[014] [15] R. Deszcz and M. Hotloś, On geodesic mappings in pseudosymmetric manifolds, Bull. Inst. Math. Acad. Sinica 16 (1988), 251-262. | Zbl 0668.53007
[015] [16] R. Deszcz and M. Hotloś, Notes on pseudosymmetric manifolds admitting special geodesic mappings, Soochow J. Math. 15 (1989), 19-27. | Zbl 0696.53014
[016] [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. | Zbl 0744.53008
[017] [18] R. Deszcz and M. Hotloś, On conformally related four-dimensional pseudosymmetric metrics, Rend. Sem. Fac. Univ. Cagliari 59 (1989), 165-175. | Zbl 0791.53022
[018] [19] R. Deszcz and M. Hotloś, On conformally related pseudosymmetric metrics, ibid., to appear. | Zbl 0852.53015
[019] [20] R. Deszcz, L. Verstraelen and L. Vrancken, On the symmetry of warped product spacetimes, Gen. Rel. Gravit. 23 (1991), 671-681. | Zbl 0723.53009
[020] [21] K. Nomizu, On the decomposition of generalized curvature tensor fields, in: Differential Geometry in honor of K. Yano, Kinokuniya, Tokyo 1972, 335-345.
[021] [22] K. Nomizu, What is affine differential geometry?, in: Proc. Differential Geom., Münster 1982, 42-43.
[022] [23] K. Nomizu, Introduction to Affine Differential Geometry, Part I, Lecture Notes, MPI preprint 88-37.
[023] [24] K. Nomizu and Ü. Pinkall, On the geometry of affine immersions, Math. Z. 195 (1987), 165-178. | Zbl 0629.53012
[024] [25] Z. Olszak, Bochner flat Kählerian manifolds with certain condition on the Ricci tensor, Simon Stevin 63 (1989), 295-303. | Zbl 0629.53059
[025] [26] B. Opozda, New affine curvature tensor and its properties, lecture given during the meeting 'Current Topics in Affine Differential Geometry', Leuven 1989.
[026] [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.
[027] [28] U. Simon, Hypersurfaces in equiaffine differential geometry, Geom. Dedicata 17 (1984), 157-168. | Zbl 0553.53004
[028] [29] U. Simon, The fundamental theorem in affine hypersurface theory, ibid. 26 (1988), 125-137. | Zbl 0641.53011
[029] [30] P. Verheyen, Hyperoppervlakken in een affiene ruimte, Ph.D. thesis, Katholieke Universiteit Leuven, 1983.
[030] [31] P. Verheyen and L. Verstraelen, Locally symmetric affine hypersurfaces, Proc. Amer. Math. Soc. 93 (1985), 101-105. | Zbl 0535.53007