Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka-Webster connection

D. L. Kiran Kumar, H. G. Nagaraja, Dipansha Kumari

Abstract


The objective of the present paper is to study concircular curvature tensor of Kenmotsu manifold with respect to generalized Tanaka-Webster connection, whose concircular curvature tensor satisifies certain conditions and it is shown that if the curvature tensor of a Kenmotsu manifold admitting generalized Tanaka-Webster connection $\nabla^{*}$ vanishes, then the Kenmotsu manifold is locally isometric to the hyperbolic space $H^{2n+1}(-1)$. Further we have studied $\xi$-concircularly flat, $\phi$-concircularly flat, pseudo-concircularly flat, $C^{*} . \phi =0$, $C^{*}.S^{*}=0$ and we have shown that $R^{*} . C^{*}=R^{*} . R^{*}$. Finally, an example of a $5$-dimensional Kenmotsu manifold with respect to the generalized Tanaka-Webster connection is given to verify our result.

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How to Cite this Article:

D. L. Kiran Kumar, H. G. Nagaraja, Dipansha Kumari, Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka-Webster connection, Journal of Mathematical and Computational Science, Vol 9, No 4 (2019), 447-462

Copyright © 2019 D. L. Kiran Kumar, H. G. Nagaraja, Dipansha Kumari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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