Title: On singular Finsler foliation,
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 $\mathcal{F}$ is a singular Finsler
foliation on a Randers manifold $(M,Z)$ with Zermelo data $(\mathtt{h},W),$
then $\mathcal{F}$ is a singular Riemannian foliation on the Riemannian
manifold $(M,\mathtt{h} )$. 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 $\mathtt{h}$
(e.,g when $W$ is killing vector field or $M$ has constant Finsler curvature).
We also present a slice theorem that relates local singular Finsler
foliations on Finsler manifolds with singular Finsler foliations on Minkowski
spaces.