ON THE $\mathcal{M}$--PROJECTIVE CURVATURE TENSOR OF A $(k, \mu)$-CONTACT METRIC MANIFOLD

D. G. Prakasha, Kakasab Mirji

DOI Number
10.22190/FUMI1701117P
First page
117
Last page
128

Abstract


The paper deals with the study of $\mathcal{M}$-projective curvature tensor on $(k, \mu)$-contact metric manifolds. We classify non-Sasakian $(k, \mu)$-contact metric manifold satisfying the conditions $R(\xi, X)\cdot \mathcal{M} = 0$ and $\mathcal{M}(\xi, X)\cdot S =0$, where $R$ and $S$ are the Riemannian curvature tensor and the Ricci tensor, respectively. Finally, we prove that a $(k, \mu)$-contact metric manifold with vanishing extended $\mathcal{M}$-projective curvature tensor $\mathcal{M}^{e}$ is a Sasakian manifold.

Keywords

(k, μ)-contact metric manifold, N(k)-contact metric manifold, Sasakian manifold, M-projective curvature tensor, Einstein manifold.

Keywords


$(k, \mu)$-contact metric manifold; $N(k)$-contact metric manifold; Sasakian manifold; $\mathcal{M}$-projective curvature tensor; Einstein manifold.

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DOI: https://doi.org/10.22190/FUMI1701117P

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