Isoparametric functions and mean curvature in manifolds with Zermelo navigation
Differential Geometry
2023-01-31 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2301.12315,
title = {Isoparametric functions and mean curvature in manifolds with Zermelo navigation},
author = {Benigno Oliveira Alves and Patricia Marcal},
journal= {arXiv preprint arXiv:2301.12315},
year = {2023}
}