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arXiv · 1808.06090

Certain results on Kenmotsu pseudo-metric manifolds

Devaraja Mallesha Naik·Venkatesha·D. G. Prakasha
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Abstract

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature, and prove the structure theorem for $\xi$-conformally flat and $\varphi$-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an $\eta$-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature $-\varepsilon$.

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Devaraja Mallesha Naik, Venkatesha, D. G. Prakasha. 2018-08-18. Certain results on Kenmotsu pseudo-metric manifolds. https://doi.org/10.18514/mmn.2019.2905

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