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Title

Certain curvature characterizations of affine hypersurfaces

Authors 1

Affiliations

  1. Department of Mathematics, Agricultural University of Wrocław, Norwida 25, 50-375 Wrocław, Poland

Bibliography

  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.
Colloquium Mathematicum
1992/63/1
Export to PBN, Opens in new tab
Pages:
21-39
Main language of publication
English
Received
1990-06-13
Published
1992
Exact and natural sciences