Stability of Certain Reflective Submanifolds in Compact Symmetric Spaces

Abstract

In [1], J. Berndt and H. Tamaru classified all the cohomogeneity one actions on Riemannian symmetric spaces of noncompact type with a totally geodesic singular orbit. Also they provided that there is a one-to-one correspondence between the totally geodesic singular orbits of cohomogeneity one actions on a Riemannian symmetric space of noncompact type and those on its dual simply connected compact Riemannian symmetric space. In this paper, we determine stability of the totally geodesic singular orbits in simply connected compact symmetric spaces which obtained by the duality stated above.