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arXiv · 2102.01257

On equifocal Finsler submanifolds and analytic maps

Marcos M. Alexandrino·Benigno Alves·Miguel Angel Javaloyes
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Abstract

A relevant property of equifocal submanifolds is that their parallel sets are still immersed submanifolds, which makes them a natural generalization of the so-called isoparametric submanifolds. In this paper, we prove that the regular fibers of an analytic map $\pi:M^{m+k}\to B^{k}$ are equifocal whenever $M^{m+k}$ is endowed with a complete Finsler metric and there is a restriction of $\pi$ which is a Finsler submersion for a certain Finsler metric on the image. In addition, we prove that when the fibers provide a singular foliation on $M^{m+k}$, then this foliation is Finsler.

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Marcos M. Alexandrino, Benigno Alves, Miguel Angel Javaloyes. 2021-02-02. On equifocal Finsler submanifolds and analytic maps. https://arxiv.org/abs/2102.01257

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