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 ×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.