ON C-BOCHNER CURVATURE TENSOR OF A CONTACT METRIC MANIFOLD

Abstract

We prove that a (k, <TEX>$\mu$</TEX>)-manifold with vanishing E­Bochner curvature tensor is a Sasakian manifold. Several interesting corollaries of this result are drawn. Non-Sasakian (k, <TEX>$\mu$</TEX>)­manifolds with C-Bochner curvature tensor B satisfying B <TEX>$(\xi,\;X)\;\cdot$</TEX> S = 0, where S is the Ricci tensor, are classified. N(K)-contact metric manifolds <TEX>$M^{2n+1}$</TEX>, satisfying B <TEX>$(\xi,\;X)\;\cdot$</TEX> R = 0 or B <TEX>$(\xi,\;X)\;\cdot$</TEX> B = 0 are classified and studied.