On $\phi$-recurrent $(k,\mu)$-contact metric manifolds
Bull. Korean Math. Soc. 2008 Vol. 45, No. 4, 689-700
Printed December 1, 2008
Jae-Bok Jun, Ahmet Yildiz, and Uday Chand De
Kookmin University, Dumlup\i nar University, and University of Kalyani
Abstract : In this paper we prove that a $\phi$-recurrent $(k,\mu)$-contact metric manifold is an $\eta$-Einstein manifold with constant coefficients. Next, we prove that a three-dimensional locally $\phi$-recurrent $(k,\mu )$-contact metric manifold is the space of constant curvature. The existence of $\phi$-recurrent $(k,\mu )$-manifold is proved by a non-trivial example.
Keywords : $(k,\mu )$-contact metric manifolds, $\eta$-Einstein manifold, $\phi$-recurrent $(k,\mu )$-contact metric manifolds
MSC numbers : 53C15, 53C40
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