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On a class of two-dimensional Finsler manifolds of isotropic S-curvature

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Abstract

For an (α, β)-metric (non-Randers type) of isotropic S-curvature on an n-dimensional manifold with non-constant norm ║β║ α , we first show that n = 2, and then we characterize such a class of two-dimensional (α, β)-manifolds with some PDEs, and also construct some examples for such a class.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11371386 and 11471226) and the European Union’s Seventh Framework Programme (FP7/2007-2013) (Grant No. 317721).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, 400054, China

    Xinyue Cheng

  2. Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, IN, 46202, USA

    Zhongmin Shen

  3. Department of Mathematics, Sichuan University, Chengdu, 610065, China

    Guojun Yang

Authors
  1. Xinyue Cheng
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  2. Zhongmin Shen
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  3. Guojun Yang
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Correspondence to Guojun Yang.

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Cheng, X., Shen, Z. & Yang, G. On a class of two-dimensional Finsler manifolds of isotropic S-curvature. Sci. China Math. 61, 57–72 (2018). https://doi.org/10.1007/s11425-016-9079-1

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  • DOI: https://doi.org/10.1007/s11425-016-9079-1

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