arXiv subjects

Patricia Marcal

Publications and source records attributed to Patricia Marcal.

3 recordsLinked to original sources

arXiv2026

On singular Finsler foliations of $(α,β)$-spaces

We investigate singular Finsler foliations (SFFs) on a manifold equipped with an $(α,β)$-metric. To be precise, we verify that any SFF of an $(α,β)$-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.

math.DG↗

arXiv2023

Ricci flat Finsler metrics by warped product

In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen, S. and Zhao (2018), with another "warping", one that is consistent with static spacetimes. We will give the PDE characterization for the proposed metrics to be Ricci-flat and explicitly construct two non-Riemannian examples.

math.DG↗

arXiv2023

Isoparametric functions and mean curvature in manifolds with Zermelo navigation

The generalized Zermelo navigation problem looks for the shortest time paths in an environment, modeled by a Finsler manifold (M,F), under the influence of wind or current, represented by a vector field W. The main objective of this paper is to investigate the relationship between the isoparametric functions on the manifold M with and without the presence of the vector field W. For the positive-definite cases, we also compare the mean curvatures in the manifold. Overall, we follow a coordinate-free approach.

math.DG↗