On some types of isoparametric hypersurfaces in spheres, II

Abstract

Introduction. This paper is a continuation of Part I In the first half of the present paper, we study the homogeneous isoparametric hyper surf aces in spheres. Every homogeneous hyper surf ace in a sphere is represented as an orbit of a linear isotropy group of a Riemannian symmetric space of rank 2, due to Hsiang-Lawson In 1, we study the linear isotropy representations of Riemannian symmetric spaces and their orbits in general. 2 and 3 are devoted to a study of the homogeneous isoparametric hyper surf aces, their classification and invariant polynomials. In 4 and 5, we construct explicitly the defining polynomial F for each homogeneous isoparametric hypersurface in a sphere, which was done by Cartan [3] in case g -3.