Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON C-BOCHNER CURVATURE TENSOR OF A CONTACT METRIC MANIFOLD

  • KIM, JEONG-SIK (DEPRTMENT OF MATHEMATICS AND MATHEMATICAL INFORMATION YOSU NATIONAL UNIVERSITY) ;
  • TRIPATHI MUKUT MANI (DEPARTMENT OF MATHEMATICS AND ASTRONOMY, LUCKNOW UNIVERSITY) ;
  • CHOI, JAE-DONG (DEPARTMENT OF MATHEMATICS, KOREA AIR FORCE ACADEMY)
  • Published : 2005.11.01
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Abstract

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.

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References

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