Communications of the
Korean Mathematical Society CKMS

We study pseudo symmetric (briefly $(PS)_{n}$) and pseudo Ricci symmetric (briefly $(PRS)_{n}$) warped product manifolds $M\times _{F}N$. 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 (\ref{T}) satisfies a certain condition.

Keywords: warped product manifold, pseudo symmetric manifold, pseudo Ricci symmetric manifold

MSC numbers: 53B35, 53B05