Isoparametric hypersurfaces in Randers space forms

TL;DR

This paper studies isoparametric hypersurfaces in Randers space forms, showing their classification aligns with the Riemannian case, and provides examples of such hypersurfaces.

Contribution

It establishes that the classification of isoparametric hypersurfaces in Randers space forms matches that in Riemannian geometry, despite differences in isoparametric functions.

Findings

Isoparametric hypersurfaces in Randers space forms are classified the same as in Riemannian geometry.

The isoparametric functions differ between BH-volume and Riemannian metrics but classify the same hypersurfaces.

Examples of isoparametric functions in Randers space forms are provided.

Abstract

In this paper, we discuss anisotropic submanifolds and isoparametric hypersurfaces in a Randers space form (N,F) with the navigation datum (h,W). We find that (N, F) with respect to the BH-volume and (N,h) have the same isoparametric hypersurfaces although, in general, their isoparametric functions are different. This implies that the classification of isoparametric hypersurfaces in a Randers space form is the same as that in Riemannian case. Lastly, we give some examples of isoparametric functions in Randers space forms.