On ricci-pseudosymmetric hypersurfaces in spaces of constant curvature

Defever F., Deszcz R., Dhooghe P., Yaprak S., Verstraelen L.

Results in Mathematics, vol.27, no.3, pp.227-236, 1995 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 3
  • Publication Date: 1995
  • Doi Number: 10.1007/bf03322827
  • Journal Name: Results in Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.227-236
  • Keywords: 53B20, 53B30, 53B50, 53C25, 53C35, 53C80, hypersurfaces, pseudosymmetric manifolds, semisymmetric manifolds
  • Ankara University Affiliated: Yes

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. © 1995, Birkhäuser Verlag, Basel. All rights reserved.