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arXiv · 2604.18795

On singular Finsler foliations of $(\alpha,\beta)$-spaces

Marcos M. Alexandrino·Benigno O. Alves·Patricia Marcal
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Abstract

We investigate singular Finsler foliations (SFFs) on a manifold equipped with an $(\alpha,\beta)$-metric. To be precise, we verify that any SFF of an $(\alpha,\beta)$-space is, under some hypotheses on the metric, a singular Riemannian foliation (SRF). This gives a partial answer to the general question "under which conditions a SFF is a SRF with respect to some Riemannian metric". Moreover, we extend the proof of Molino's conjecture to SFFs whenever they are also a SRFs. Finally, we prove equifocality of the regular leaves for a SFF under the same condition.

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Marcos M. Alexandrino, Benigno O. Alves, Patricia Marcal. 2026-04-20. On singular Finsler foliations of $(\alpha,\beta)$-spaces. https://arxiv.org/abs/2604.18795

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