Skip to main content
SpringerLink
Log in

Pseudosymmetry Curvature Conditions Imposed on the shape Operators of Hypersurfaces in the Affine space

  • Published:
Results in Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A, Adamów and R. Deszcz. On totally umbilical submanifolds of some class of Riemannian manifolds, Demonstratio Math., 16(1983) 39–59.

    MathSciNet  MATH  Google Scholar 

  2. F. Defever and R. Deszcz, On warped product manifolds satisfying a certain curvature condition, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur., in print.

  3. F. Defever and R. Deszcz, On semi-Rieraannian manifolds satisfying the condition R·R = Q(S,R), in Geometry and Topology of Submanifolds, III, Leeds, May 1990, World Sci. Publ., in print.

  4. F. Defever and R. Deszcz, A note on geodesic mappings of pseudosymmetric manifolds, Colloquium Math., in print.

  5. 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.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudo-symmetric conformally flat warped products, Chinese J. Math., 17(1989)51–65.

    MathSciNet  MATH  Google Scholar 

  7. R. Deszcz, Notes on totally umbilical submanifolds, in Geometry and Topology of Submanifolds, Luminy, May 1987, World Sci. Publ., Singapore 1989, 89–97.

  8. R. Deszcz, On pseudosymmetric totally umbilical submanifolds of Riemannian manifolds admitting some types of generalized curvature tensors, Zesz. Nauk. Pol. s1., in print.

  9. R. Deszcz, On pseudosymmetric warped product manifolds, to appear.

  10. R. Deszcz, On conformally flat Riemannian manifolds satisfying certain curvature conditions. Tensor, N.S., in print.

  11. R. Deszcz, Certain curvature characterizations of affine hypersurfaces. Colloquium Math., in print.

  12. R. Deszcz and W. Grycak, On some class of warped product manifolds. Bull. Inst. Math. Acad. Sinica, 15(1987) 311–322.

    MathSciNet  MATH  Google Scholar 

  13. R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, Colloquium Math., 58(1990) 259–268.

    MathSciNet  MATH  Google Scholar 

  14. R. Deszcz and M. Hotloé, On geodesic mappings in pseudosymmetric manifolds, Bull. Inst. Math. Acad. Sinica, 16(1988) 251–262.

    MathSciNet  MATH  Google Scholar 

  15. R. Deszcz and M. Hotloé, Notes on pseudosymmetric manifolds admitting special geodesic mappings, Soochow J. Math., 15 (1989) 19–27.

    MathSciNet  MATH  Google Scholar 

  16. R. Deszcz and L. Verstraelen, Hypersurfaces of semi-Riemannian conformally flat manifolds, in Geometry and Topology of Submanifolds, III, Leeds, May 1990, World Sci, Publ., in print.

  17. R. Deszcz, L. Verstraelen and L. Vrancken, On the symmetry of warped product spacetimes. General Relativity and Gravitation, in print.

  18. L.P. Eisenhart, Riemannian geometry, Princeton 1966.

  19. Yu. G. Lumiste, Semisymmetric manifolds (in Russian), Problems of geometry, 23 (1991), in print.

  20. J. Mikesh, Geodesic mappings of special Riemannian spaces, Topics in differential geometry, Vol I-II Dedrecen, 1984 798–813. Colloq. Math. Soc. Janos Bolyai, 46, North-Holland, Amsterdam-New York, 1988.

  21. V.A. Mirzoyan, Ric-semisymmetric submanifolds (in Russian), Problems of geometry, 23 (1991), in print.

  22. K. Nomizu, On the decomposition of generalized curvature tensor fields, Differential Geometry in honor of K. Yano. Kinokuniya, Tokyo 1972, 335–345.

  23. K. Nomizu, A survey of recent results in affine differential geometry, in Geometry and Topology of Submanifolds, III, Leeds, May 1990, World Sci. Publ., in print

  24. B. Opozda, New affine curvature tensor and its properties. The lecture given during the meeting “Current topics in affine differential geometry”, Leuven, 1989.

  25. B. Opozda and L. Verstraelen, On a new curvature tensor in affine differential geometry, in Geometry and Topology of Submanifolds, II, Avignon, May 1988, World Sci. Publ., Singapore, 1990, 271–293.

  26. Z.I. Szabó, Structure theorems on Riemannian spaces satisfying R(X,Y)·R = 0. I. The local version, J. Diff. Geom., 17(1982) 531–582.

    MATH  Google Scholar 

  27. Z.I. Szabó, Classification and construction of complete hypersurfaces satisfying R(X,Y)·R = 0, Acta Sci. Math., 47(1984) 321–348.

    MATH  Google Scholar 

  28. Z.I. Szabó, Structure theorems on Riemannian spaces satisfying R(X,Y)·R = 0, II. Global versions, Geom. Dedicata, 19(1985) 65–108.

    Article  MathSciNet  MATH  Google Scholar 

  29. I. Van de Woestijne, Semisymmetric hypersurfaces, in Geometry and Topology of Submanifolds, Luminy, May 1987, World Sci. Publ., Singapore 1989, 231–244.

    Google Scholar 

  30. I. Van de Woestijne, Semisymmetric Lorentzian hypersurfaces. The local version, to appear.

  31. I. Van de Woestijne and L. Verstraelen, Semisymmetric Lorentzian hypersurfaces, Tohoku Math. 3., 39(1987) 81–88.

    Google Scholar 

  32. L. Vrancken, Affine quasi-umbilical hypersurfaces which are flat with respect to the affine metric, to appear.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Agricultural Academy, ul. C. Norwida 25, 50-375, Wroclaw, Poland

    Ryszard Deszcz

Authors
  1. Ryszard Deszcz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deszcz, R. Pseudosymmetry Curvature Conditions Imposed on the shape Operators of Hypersurfaces in the Affine space. Results. Math. 20, 600–621 (1991). https://doi.org/10.1007/BF03323198

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03323198

Keywords

Search

Navigation