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Isoparametric functions and mean curvature in manifolds with Zermelo navigation (2301.12315v1)
Published 29 Jan 2023 in math.DG
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.