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Finsler warped product metrics with special Riemannian curvature properties

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Abstract

One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant (or scalar) curvature. In this paper, we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metrics of scalar flag curvature. In particular, we find equations that characterize Finsler warped product metrics of constant flag curvature. Then we improve the Chen-Shen-Zhao result on characterizing Einstein Finsler warped product metrics. As its application we construct explicitly many new warped product Douglas metrics of constant Ricci curvature by using known locally projectively flat spherically symmetric metrics of constant flag curvature.

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Acknowledgements

This work was supported by Beijing Natural Science Foundation (Grant No. 1182006) and National Natural Science Foundation of China (Grant No. 11771020).

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China

    Huaifu Liu & Hongzhen Zhang

  2. Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Xiaohuan Mo

Authors
  1. Huaifu Liu
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  2. Xiaohuan Mo
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  3. Hongzhen Zhang
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Correspondence to Xiaohuan Mo.

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Liu, H., Mo, X. & Zhang, H. Finsler warped product metrics with special Riemannian curvature properties. Sci. China Math. 63, 1391–1408 (2020). https://doi.org/10.1007/s11425-018-9422-4

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  • DOI: https://doi.org/10.1007/s11425-018-9422-4

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