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Certain results on almost contact pseudo-metric manifolds

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Abstract

We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields \(h:=\frac{1}{2}\pounds _\xi \varphi \) and \(\ell := R(\cdot ,\xi )\xi \), emphasizing analogies and differences with respect to the contact metric case. Certain identities involving \(\xi \)-sectional curvatures are obtained. We establish necessary and sufficient condition for a nondegenerate almost CR structure \((\mathcal {H}(M), J, \theta )\) corresponding to almost contact pseudo-metric manifold M to be CR manifold. Finally, we prove that a contact pseudo-metric manifold \((M, \varphi ,\xi ,\eta ,g)\) is Sasakian pseudo-metric if and only if the corresponding nondegenerate almost CR structure \((\mathcal {H}(M), J)\) is integrable and J is parallel along \(\xi \) with respect to the Bott partial connection.

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Acknowledgements

The authors would like to thank the reviewer for careful and thorough reading of this manuscript and thankful for helpful suggestions towards the improvement of this paper. The second author (D.M.N.) is grateful to University Grants Commission, New Delhi (Ref. No.: 20/12/2015(ii)EU-V) for financial support in the form of Junior Research Fellowship.

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Correspondence to V. Venkatesha.

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Venkatesha, V., Naik, D.M. & Tripathi, M.M. Certain results on almost contact pseudo-metric manifolds. J. Geom. 110, 41 (2019). https://doi.org/10.1007/s00022-019-0498-7

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  • DOI: https://doi.org/10.1007/s00022-019-0498-7

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