ON CURVATURE PROPERTIES OF CERTAIN QUASI-EINSTEIN HYPERSURFACES-Reference-Cited by-同舟云学术

ON CURVATURE PROPERTIES OF CERTAIN QUASI-EINSTEIN HYPERSURFACES

Published:2012-06-27 Issue:07 Volume:23 Page:1250073
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

DESZCZ RYSZARD¹,HOTLOŚ MARIAN²,ṢENTÜRK ZERRIN³

Affiliation:

1. Department of Mathematics, Wrocław University of Environmental and Life Sciences, Grunwaldzka 53 PL 50-357, Wrocław, Poland

2. Institute of Mathematics and Informatics, Wrocław University of Technology, Wybrzeze Wyspiańskiego 27 PL 50-357, Wrocław, Poland

3. Mathematics Engineering Department, Faculty of Science and Letters, Istanbul Technical University, Maslak, TR-34469, İstanbul, Turkey

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X12500735

Reference31 articles.

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