Some geometric correspondences for homothetic navigation

TL;DR

This paper explores geometric correspondences in homothetic navigation, providing explanations and shortcuts to curvature formulas, and generalizing classifications of isoparametric hypersurfaces in specific Finsler spaces.

Contribution

It offers conceptual insights into geodesic and Jacobi field correspondences, leading to new shortcuts for curvature formulas and extending classification results in Finsler geometry.

Findings

Derived new curvature formulas using geometric correspondences

Connected isoparametric functions with homothetic navigation

Generalized classification of isoparametric hypersurfaces in Finsler spaces

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.