A Filtration for Isoparametric Hypersurfaces in Riemannian Manifolds

TL;DR

This paper defines and explores the properties of k-isoparametric hypersurfaces in Riemannian manifolds, providing new results towards their classification in various symmetric spaces.

Contribution

It introduces the concept of k-isoparametric hypersurfaces and advances their classification in complex and symmetric Riemannian spaces.

Findings

New characterization of k-isoparametric hypersurfaces

Results towards classification in complex projective and hyperbolic spaces

Insights into homogeneous hypersurfaces in symmetric spaces

Abstract

This paper introduces the notion of $k$-isoparametric hypersurface in an $(n+1)$-dimensional Riemannian manifold for $k=0,1,...,n$. Many fundamental and interesting results (towards the classification of homogeneous hypersurfaces among other things) are given in complex projective spaces, complex hyperbolic spaces, and even in locally rank one symmetric spaces.