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Static perfect fluid space-time on contact metric manifolds

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Abstract

The purpose of this article is to study the characteristics of static perfect space-time metrics on contact metric manifolds. At first we prove that if a complete K-contact metric manifold is the spatial factor of static perfect space-time, then it is isometric to a round sphere. For a three dimensional contact metric manifold, which is the spatial factor of static perfect space-time, we show that it is Einstein if its Ricci tensor is commuting. Next we consider static perfect space-time \((\kappa ,\mu ,\nu )\)-contact metric manifolds and give some characteristics under certain conditions.

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Acknowledgements

The authors would like to thank the referee for the valuable comments on this paper.

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  1. College of Science, China University of Petroleum-Beijing, Beijing, 102249, China

    Xiaomin Chen & Yifan Yang

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  1. Xiaomin Chen
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  2. Yifan Yang
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Correspondence to Xiaomin Chen.

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The author is supported by Science Foundation of China University of Petroleum-Beijing (Nos. 2462020XKJS02, 2462020YXZZ004)

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Chen, X., Yang, Y. Static perfect fluid space-time on contact metric manifolds. Period Math Hung 86, 160–171 (2023). https://doi.org/10.1007/s10998-022-00466-6

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