Some geometric correspondences for homothetic navigation
Differential Geometry
2021-06-08 v2
Abstract
In this paper, we provide conceptional explanations for the geodesic and Jacobi field correspondences for homothetic navigation, and then let them guide us to the shortcuts to some well known flag curvature and S-curvature formulas. They also help us directly see the local correspondence between isoparametric functions or isoparametric hypersurfaces, which generalizes the classification works of Q. He and her coworkers for isoparametric hypersurfaces in Randers space forms and Funk spaces.
Keywords
Cite
@article{arxiv.1910.07435,
title = {Some geometric correspondences for homothetic navigation},
author = {Ming Xu and Vladimir Matveev and Ke Yan and Shaoxiang Zhang},
journal= {arXiv preprint arXiv:1910.07435},
year = {2021}
}
Comments
In version 2, the proofs of some lemmas have been refined or shortened