Pseudo symmetric and pseudo ricci symmetric warped product manifolds

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.