A filtration for isoparametric hypersurfaces in Riemannian manifolds

Abstract

Motivated by the well known Cartan-Munzner equations and the Chern conjecture, we introduce the notion of k-isoparametric hypersurface in an (n + 1)- dimensional Riemannian manifold for k = 0,1,...,n. Many fundamental and inter- esting 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. Further investigations in this direction are expected.