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DOI QR Code

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

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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  3. E-Bochner curvature tensor on generalized Sasakian space forms vol.354, pp.8, 2016, https://doi.org/10.1016/j.crma.2015.10.027
  4. Pinching Theorems for a Vanishing C-Bochner Curvature Tensor vol.6, pp.11, 2018, https://doi.org/10.3390/math6110231