Browsing by Subject "Randers spaces"

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    On singular Finsler foliation
    (Springer, 2018-07-04) Alexandrino, Marcos M.; Alves, Benigno O.; Javaloyes Victoria, Miguel Ángel; Matemáticas
    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.