PSEUDO SYMMETRIC AND PSEUDO RICCI SYMMETRIC WARPED PRODUCT MANIFOLDS


DE U. C. , MURATHAN C. , ÖZGÜR C.

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, vol.25, no.4, pp.615-621, 2010 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.4134/ckms.2010.25.4.615
  • Title of Journal : COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.615-621
  • Keywords: warped product manifold, pseudo symmetric manifold, pseudo Ricci symmetric manifold

Abstract

We study pseudo symmetric (briefly (PS)(n)) and pseudo Ricci symmetric (briefly (PRS)(n)) warped product manifolds M x (F) N. If M is (PS)(n), then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is (PRS)(n), then we show that (i) N is Ricci symmetric and (ii) M is (PRS)(n) if and only if the tensor T defined by (2.6) satisfies a certain condition.