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Results in Mathematics

, Volume 27, Issue 3–4, pp 227–236 | Cite as

On ricci-pseudosymmetric hypersurfaces in spaces of constant curvature

  • Filip Defever
  • Ryszard Deszcz
  • Paul Dhooghe
  • Sahnur Yaprak
  • Leopold Verstraelen
Article

Abstract

This article studies the conditions of pseudosymmetry and Ricci-pseudosymmetry, realizedon hypersurfaces of semi-Riemannian spaces of constant curvature. In particular, we derive extrinsic characterizations of pseudosymmetric and Ricci-pseudosymmetric hypersurfaces of semi-Riemannian spaces of constant curvature in terms of the shape operator. As an application, and in the Riemannian case, we extend a theorem by K. Nomizu on semisymmetric hypersurfaces of Euclidean spaces.

Keywords

semisymmetric manifolds pseudosymmetric manifolds hypersurfaces 

Math. Subject Classification

53B20 53B30 53B50 53C25 53C35 53C80 

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References

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Copyright information

© Birkhäuser Verlag, Basel 1995

Authors and Affiliations

  • Filip Defever
    • 1
  • Ryszard Deszcz
    • 2
  • Paul Dhooghe
    • 3
  • Sahnur Yaprak
    • 4
  • Leopold Verstraelen
    • 5
    • 6
  1. 1.Departement NatuurkundeInstituut voor theoretische fysicaLeuvenBelglum
  2. 2.Department of MathematicsAgricultural University of WroclawulWroclawPoland
  3. 3.Departement Wiskunde K.U. LeuvenLeuven Belgium
  4. 4.Department of MathematicsUniversity of AnkaraTandoganTurkey
  5. 5.Departement WiskundeLeuvenBelgium
  6. 6.Departement EconomieBrusselBelgium

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