Isoparametric hypersurfaces of conic Finsler manifolds

TL;DR

This paper introduces and classifies isoparametric hypersurfaces in conic Finsler spaces, revealing new types beyond classical examples and providing a complete classification in specific Kropina spaces.

Contribution

It defines isoparametric hypersurfaces in conic Finsler spaces and classifies them in Kropina spaces with constant flag curvature, identifying new examples like helicoids.

Findings

Conic Minkowski hyperplanes, hyperspheres, and cylinders are isoparametric.

Potential existence of other isoparametric hypersurfaces such as helicoids.

Complete classification of isoparametric hypersurfaces in Kropina spaces with constant flag curvature.

Abstract

In this paper, we introduce isoparametric functions and isoparametric hypersurfaces in conic Finsler spaces. We find that in a conic Minkowski space, besides the conic Minkowski hyperplanes, conic Minkowski hyperspheres and conic Minkowski cylinders, which are all isoparametric hypersurfaces, there are probably other isoparametric hypersurfaces, such as helicoids. Moreover, we give a complete classification of isoparametric hypersurfaces in kropina spaces with constant flag curvature.