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Title

On Weyl pseudosymmetric hypersurfaces

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, Uludağ University, Gorükle Kampüsü, Bursa, Turkey
  2. Department of Mathematics, Agricultural University of Wrocław, ul. Grunwaldzka 53, 50-357 Wrocław, Poland
  3. Department of Mathematics, University of Ankara, 06100 Tandoğan, Ankara, Turkey

Bibliography

  1. T. E. Cecil and P. J. Ryan, Tight and Taut Immersions of Manifolds, Pitman, Boston, 1988.
  2. F. Defever, R. Deszcz, P. Dhooghe, L. Verstraelen and Ş. Yaprak, On Ricci-pseudosymmetric hypersurfaces in spaces of constant curvature, Results in Math. 27 (1995), 227-236.
  3. F. Defever, R. Deszcz, Z. Şentürk, L. Verstraelen and Ş. Yaprak, P. J. Ryan's problem in semi-Euclidean space, to appear.
  4. J. Deprez, R. Deszcz and L. Verstraelen, Pseudo-symmetry curvature conditions on hypersurfaces of Euclidean spaces and on Kählerian manifolds, Ann. Fac. Sci. Toulouse 9 (1988), 183-192.
  5. J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudo-symmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65.
  6. A. Derdziński, Exemples de métriques de Kaehler et d'Einstein autoduales sur le plan complexe, in: Géométrie riemannienne en dimension 4 (Séminaire Arthur Besse 1978/79), Cedic/Fernand Nathan, Paris, 1981, 334-346.
  7. R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065.
  8. R. Deszcz, Examples of four-dimensional Riemannian manifolds satisfying some pseudosymmetry curvature conditions, in: Geometry and Topology of Submanifolds 2, World Sci., Singapore, 1990, 134-143.
  9. R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudosymmetry curvature conditions, Colloq. Math. 62 (1991), 103-120.
  10. R. Deszcz, Pseudosymmetry curvature conditions imposed on the shape operators of hypersurfaces in the affine spaces, Results in Math. 20 (1991), 600-621.
  11. R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Sér. A 44 (1992), 1-34.
  12. R. Deszcz, Curvature properties of a certain compact pseudosymmetric manifold, Colloq. Math. 65 (1993), 139-147.
  13. R. Deszcz, On pseudosymmetric manifolds, Dept. Math., Agricultural Univ. Wrocław, Preprint No. 34, 1995.
  14. R. Deszcz, On certain classes of hypersurfaces in spaces of constant curvature, in: Geometry and Topology of Submanifolds 8, World Sci., Singapore, 1996, in print.
  15. R. Deszcz, S. Ewert-Krzemieniewski and J. Policht, On totally umbilical submanifolds of conformally birecurrent manifolds, Colloq. Math. 55 (1988), 79-96.
  16. R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322.
  17. R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92.
  18. R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268.
  19. R. Deszcz and M. Hotloś, Remarks on Riemannian manifolds satisfying a certain curvature condition imposed on the Ricci tensor, Prace Nauk. Pol. Szczec. 11 (1989), 23-34.
  20. R. Deszcz and M. Hotloś, Notes on pseudo-symmetric manifolds admitting special geodesic mappings, Soochow J. Math. 15 (1989), 19-27.
  21. R. Deszcz and L. Verstraelen, Hypersurfaces of semi-Riemannian conformally flat manifold, in: Geometry and Topology of Submanifolds 3, Singapore, 1991, 131-147.
  22. R. Deszcz, L. Verstraelen and Ş. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional spaces of constant curvature, Bull. Inst. Math. Acad. Sinica 22 (1994), 167-179.
  23. R. Deszcz, L. Verstraelen and Ş. Yaprak, Hypersurfaces with pseudosymmetric Weyl tensor in conformally flat manifolds, Dept. Math. Agricultural Univ. Wrocław, preprint No. 32, 1995.
  24. R. Deszcz and Ş. Yaprak, Curvature properties of Cartan hypersurfaces, Colloq. Math. 67 (1994), 91-98.
  25. R. Deszcz and Ş. Yaprak, Curvature properties of certain pseudosymmetric manifolds, Publ. Math. Debrecen 45 (1994), 333-345.
  26. W. Grycak, Riemannian manifolds with a symmetry condition imposed on the 2-nd derivative of the conformal curvature tensor, Tensor (N.S.) 46 (1987), 287-290.
  27. Ü. Pinkall, Dupin hypersurfaces, Math. Ann. 270 (1985), 427-440.
  28. L. Verstraelen, Comments on pseudo-symmetry in the sense of Ryszard Deszcz, in: Geometry and Topology of Submanifolds 6, World Sci., Singapore, 1994, 199-209.
Colloquium Mathematicum
1997/72/2
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Pages:
353-361
Main language of publication
English
Received
1995-12-08
Accepted
1996-08-14
Published
1997
Exact and natural sciences