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arXiv · 1507.04219

Isoparametric Hypersurfaces in Minkowski Spaces

Qun He·SongTing Yin·YiBing Shen
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Abstract

In this paper, we introduce isoparametric functions and isoparametric hypersurfaces in Finsler manifolds and give the necessary and sufficient conditions for a transnormal function to be isoparametric. We then prove that hyperplanes, Minkowski hyperspheres and $F^*$-Minkowski cylinders in a Minkowski space with $BH$-volume (resp. $HT$-volume) form are all isoparametric hypersurfaces with one and two distinct constant principal curvatures respectively. Moreover, we give a complete classification of isoparametric hypersurfaces in Randers-Minkowski spaces and construct a counter example, which shows that Wang's Theorem B in \cite{WQ} does not hold in Finsler geometry.

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Qun He, SongTing Yin, YiBing Shen. 2015-07-15. Isoparametric Hypersurfaces in Minkowski Spaces. https://arxiv.org/abs/1507.04219

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