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Classifications of Isoparametric Hypersurfaces in Randers Space Forms

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Abstract

In this paper, we give the complete classifications of isoparametric hypersurfaces in Randers space forms. By studying the principal curvatures of anisotropic submanifolds in a Randers space (N, F) with the navigation data (h, W), we find that a Randers space form (N, F, dµBH) and the corresponding Riemannian space (N, h) have the same isoparametric hypersurfaces, but in general, their isoparametric functions are different. We give a necessary and sufficient condition for an isoparametric function of (N, h) to be isoparametric on (N, F, dµBH), from which we get some examples of isoparametric functions.

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Acknowledgements

The authors would like to thank the referees for their time and valuable comments.

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Authors and Affiliations

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

    Qun He & Pei Long Dong

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

    Song Ting Yin

  3. Key Laboratory of Applied Mathematics (Putian University), Fujian Province University, Putian, 351100, P.R. China

    Song Ting Yin

Authors
  1. Qun He
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  2. Pei Long Dong
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  3. Song Ting Yin
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Correspondence to Song Ting Yin.

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Supported by NNSFC (Grant Nos. 11471246 and 11971253), AHNSF (Grant No. 1608085MA03) and KLAMFJPU (Grant No. SX201805)

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He, Q., Dong, P.L. & Yin, S.T. Classifications of Isoparametric Hypersurfaces in Randers Space Forms. Acta. Math. Sin.-English Ser. 36, 1049–1060 (2020). https://doi.org/10.1007/s10114-020-9324-2

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  • DOI: https://doi.org/10.1007/s10114-020-9324-2

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