The isoparametric functions on a class of Finsler spheres

TL;DR

This paper explores the structure of isoparametric functions and geodesics on Randers spheres using navigation techniques, providing explicit formulas, examples, and classifications of these geometric objects.

Contribution

It offers the first comprehensive analysis of isoparametric functions on Randers spheres, including explicit expressions and new examples of geometric structures.

Findings

Explicit formulas for geodesics and isoparametric functions on Randers spheres.

Classification of isoparametric families and focal submanifolds.

Examples of closed and non-closed geodesics and associated structures.

Abstract

In this paper, we give global expressions of geodesics and isoparametric functions on a Randers sphere by navigation. We obtain isoparametric families and focal submanifolds in (S^{n}; F; d\mu_{BH}) by Cartan-M\"unzner polynomials. Further more, we construct some examples of closed and non-closed geodesics, isoparametric functions, isoparametric families and focal submanifolds.