Actions of Hermann type and proper complex equifocal submanifolds

Abstract

In this paper, we mainly prove that principal orbits of an action of Hermann type on a symmetric space of non-compact type are curvature adapted and proper complex equifocal. The proof is performed by showing that principal orbits of the action are partial tubes over a totally geodesic singular orbit and investingating the shape operatores of the partial tubes over a submanifold in a symmetric space of non-compact type.