ON C-BOCHNER CURVATURE TENSOR OF A CONTACT METRIC MANIFOLD

We prove that a (k, $\mu$)-manifold with vanishing E­Bochner curvature tensor is a Sasakian manifold. Several interesting corollaries of this result are drawn. Non-Sasakian (k, $\mu$)­manifolds with C-Bochner curvature tensor B satisfying B $(\xi,\;X)\;\cdot$ S = 0, where S is the Ricci tensor, are...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2005, 42(4), , pp.713-724
Main Authors: KIM, JEONG-SIK, TRIPATHI MUKUT MANI, CHOI, JAE-DONG
Format: Article
Language:Korean
Subjects:
수학
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Summary:We prove that a (k, $\mu$)-manifold with vanishing E­Bochner curvature tensor is a Sasakian manifold. Several interesting corollaries of this result are drawn. Non-Sasakian (k, $\mu$)­manifolds with C-Bochner curvature tensor B satisfying B $(\xi,\;X)\;\cdot$ S = 0, where S is the Ricci tensor, are classified. N(K)-contact metric manifolds $M^{2n+1}$, satisfying B $(\xi,\;X)\;\cdot$ R = 0 or B $(\xi,\;X)\;\cdot$ B = 0 are classified and studied.
ISSN:1015-8634
2234-3016