On $C$-Bochner curvature tensor of a contact metric manifold
Bull. Korean Math. Soc. 2005 Vol. 42, No. 4, 713-724
Published online December 1, 2005
Jeong-Sik Kim, Mukut Mani Tripathi, and Jaedong Choi
Mathematical Information Yosu National University, Lucknow University, Korea Air Force Academy
Abstract : We prove that a $(\kappa ,\mu )$-manifold with vanishing $E$-Bochner curvature tensor is a Sasakian manifold. Several interesting corollaries of this result are drawn. Non-Sasakian $(\kappa ,\mu )$-manifolds with $C$-Bochner curvature tensor $B$ satisfying $B\left( \xi ,X\right) \cdot S=0$, where $S$ is the Ricci tensor, are classified. $% N(\kappa )$-contact metric manifolds $M^{2n+1}$, satisfying $B\left( \xi ,X\right) \cdot R=0$ or $B\left( \xi ,X\right) \cdot B=0$ are classified and studied.
Keywords : contact metric manifold, $(\kappa,\mu )$-manifold, $N(\kappa )$-contact metric manifold, Sasakian manifold, $C $-Bochner curvature tensor, $E$-Bochner curvature tensor, $\eta $-Einstein manifold, Einstein manifold
MSC numbers : 53C50, 53B30
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