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http://dx.doi.org/10.5666/KMJ.2016.56.3.979

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

Mallick, Sahanous (Department of Mathematics, Chakdaha College)
De, Uday Chand (Department of Pure Mathematics, University of Calcutta)
Publication Information
Kyungpook Mathematical Journal / v.56, no.3, 2016 , pp. 979-991 More about this Journal
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
k-nullity distribution; quasi-Einstein manifolds; N(k)-quasi-Einstein manifolds; Z tensor; projective curvature tensor; conformal curvature tensor;
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Times Cited By KSCI : 2  (Citation Analysis)
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