Pseudo symmetric and pseudo Ricci symmetric warped product manifolds
Commun. Korean Math. Soc. 2010 Vol. 25, No. 4, 615-621
https://doi.org/10.4134/CKMS.2010.25.4.615
Printed December 1, 2010
Uday Chand De, Ceng\.{i}zhan\ Murathan, and C\.{i}han \{O}zg\
35-Ballygunj Circular Road, Uluda\u{g} University, Bal\i kesir University
Abstract : 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
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