ON CURVATURE PROPERTIES OF CERTAIN QUASI-EINSTEIN HYPERSURFACES


Deszcz R., Hotlos M., Şentürk Z.

INTERNATIONAL JOURNAL OF MATHEMATICS, vol.23, no.7, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 7
  • Publication Date: 2012
  • Doi Number: 10.1142/s0129167x12500735
  • Title of Journal : INTERNATIONAL JOURNAL OF MATHEMATICS

Abstract

It is known that the Cartan hypersurfaces of dimension 6, 12 or 24 are non-quasi-Einstein, non-pseudosymmetric, Ricci-pseudosymmetric manifolds. In this paper we investigate quasi-Einstein hypersurfaces in semi-Riemannian space forms satisfying some Walker type identity. Among other things we prove that such hypersurfaces are Ricci-pseudosymmetric manifolds. Using certain result of Magid we construct an example of a quasi-Einstein non-pseudosymmetric Ricci-pseudosymmetric warped product which locally can be realized as a hypersurface in a semi-Riemannian space of constant curvature. In our opinion it is a first example of a hypersurface having the mentioned properties.