A classification of $(k,\mu )$-contact metric manifolds
Commun. Korean Math. Soc. 2012 Vol. 27, No. 2, 327-339
Printed June 1, 2012
Ahmet Yildiz and Uday Chand De
Dumlup\i nar University, University of Calcutta
Abstract : In this paper we study $h$-projectively semisymmetric, $\phi $-projectively semisymmetric, $h$-Weyl semisymmetric and $\phi $-Weyl semisymmetric non-Sasakian $(k,\mu )$-contact metric manifolds. In all the cases the manifold becomes an $\eta $-Einstein manifold. As a consequence of these results we obtain that if a $3$-dimensional non-Sasakian $(k,\mu )$-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an $N(k)$-contact metric manifold.
Keywords : semisymmetric spaces, $(k,\mu )$-contact metric manifolds, non-Sasakian manifolds, $\eta $-Einstein manifolds, $h$-projectively semisymmetric, $\phi $-projectively semisymmetric, $h$-Weyl semisymmetric, $\phi $-Weyl semisymmetric
MSC numbers : 53C25, 53C35, 53D10
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