Isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in Finsler spaces

TL;DR

This paper explores the properties and examples of isoparametric hypersurfaces and hypersurfaces with constant principal curvatures within Finsler spaces, focusing on Randers manifolds with varying curvature.

Contribution

It provides new examples of such hypersurfaces in Randers manifolds and constructs a conformally flat Randers space with nonisoparametric hyperplanes having constant principal curvatures.

Findings

Examples of isoparametric hypersurfaces with varying principal curvatures

Construction of a conformally flat Randers manifold with nonisoparametric hyperplanes

Analysis of hypersurfaces in Finsler spaces with constant principal curvatures

Abstract

In this paper, we study the relationship between isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in Finsler spaces. We give some examples of isoparametric hypersurfaces with (non)constant principal curvatures on Randers manifolds with nonconstant flag curvatures. Furthermore, we construct an example of a conformally flat Randers manifold which admits a family of nonisoparametric hyperplanes with constant principal curvatures.