Publication: On singular Finsler foliation
Authors
Alexandrino, Marcos M. ; Alves, Benigno O. ; Javaloyes Victoria, Miguel Ángel
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Publisher
Springer
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DOI
https://doi.org/10.1007/s10231-018-0769-1
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info:eu-repo/semantics/article
Description
© 2018, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature. This document is the Published Manuscript, version of a Published Work that appeared in final form in Annali di Matematica Pura ed Applicata. To access the final edited and published work see https://doi.org/10.1007/s10231-018-0769-1
Abstract
In this paper we introduce the concept of singular Finsler foliation, which generalizes the concepts of Finsler actions, Finsler submersions and (regular) Finsler foliations. We show that if F is a singular Finsler foliation with closed leaves on a Randers manifold (M, Z) with Zermelo data (h, W ), then F is a singular Riemannian foliation on the Riemannian manifold (M,h). As a direct consequence, we infer that the regular leaves are equifocal submanifolds (a generalization of isoparametric submanifolds) when the wind W is an infinitesimal homothety of h (e.g., when W is a Killing vector field or M has constant Finsler curvature). We also present a slice theorem that locally relates singular Finsler foliations on Finsler manifolds with singular Finsler foliations on Minkowski spaces.
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Citation
Annali di Matematica Pura ed Applicata, 2019, Vol. 198, pp. 205-226
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