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 π: Mm+k → Bk are equifocal whenever Mm+k is endowed with a complete Finsler metric and there is a restriction of π 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 Mm+k, then this foliation is Finsler.
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The first and second authors were supported by Fundação de Amparo a Pesquisa do Estado de São Paulo-FAPESP (Tematicos: 2016/23746-6). The second author was supported by CNPq (PhD fellowship) and partially supported by PDSE-Capes (PhD sandwich program). The third author was partially supported by the project PGC2018-097046-B-I00 funded by MCIN/AEI/10.13039/501100011033/FEDER “Una manera de hacer Europa” and Fundación Séneca project with reference 19901/GERM/15. This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Science and Technology Agency of the Región de Murcia.
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Alexandrino, M.M., Alves, B. & Javaloyes, M.A. On equifocal Finsler submanifolds and analytic maps. Isr. J. Math. 259, 203–237 (2024). https://doi.org/10.1007/s11856-023-2524-6
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DOI: https://doi.org/10.1007/s11856-023-2524-6