Kyungpook Mathematical Journal

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𝒡 Tensor on N(k)-Quasi-Einstein Manifolds

  • Received : 2015.06.19
  • Accepted : 2016.07.06
  • Published : 2016.09.23
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Abstract

The object of the present paper is to study N(k)-quasi-Einstein manifolds. We study an N(k)-quasi-Einstein manifold satisfying the curvature conditions $R({\xi},X){\cdot}Z=0$, $Z(X,{\xi}){\cdot}R=0$, and $P({\xi},X){\cdot}Z=0$, where R, P and Z denote the Riemannian curvature tensor, the projective curvature tensor and Z tensor respectively. Next we prove that the curvature condition $C{\cdot}Z=0$ holds in an N(k)-quasi-Einstein manifold, where C is the conformal curvature tensor. We also study Z-recurrent N(k)-quasi-Einstein manifolds. Finally, we construct an example of an N(k)-quasi-Einstein manifold and mention some physical examples.

Keywords

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