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Isoparametric hypersurfaces in Funk spaces

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Abstract

Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in Funk spaces has at most two distinct principal curvatures. Moreover, a complete classification of isoparametric families in a Funk space is given.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 11471246), Anhui Provincial Natural Science Foundation (Grant No. 1608085MA03) and Natural Science Foun- dation of Higher Education in Anhui Province (Grant No. KJ2014A257).

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Authors and Affiliations

  1. School of Mathematical Sciences, Tongji University, Shanghai, 200092, China

    Qun He

  2. Department of Mathematics and Computer Science, Tongling University, Tongling, 244000, China

    SongTing Yin

  3. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    YiBing Shen

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  1. Qun He
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  2. SongTing Yin
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  3. YiBing Shen
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Correspondence to SongTing Yin.

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He, Q., Yin, S. & Shen, Y. Isoparametric hypersurfaces in Funk spaces. Sci. China Math. 60, 2447–2464 (2017). https://doi.org/10.1007/s11425-016-8001-5

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  • DOI: https://doi.org/10.1007/s11425-016-8001-5

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