Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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PSEUDO SYMMETRIC AND PSEUDO RICCI SYMMETRIC WARPED PRODUCT MANIFOLDS

  • Received : 2009.10.16
  • Published : 2010.10.31
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Abstract

We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. 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.

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