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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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