On focal points of submanifolds in symmetric spaces

Abstract

The first purpose of this paper is to give a smart proof of the Morse index theorem for squared distance function of submanifolds in s a symmetric space. The second purpose is to classify focal points into strong ones and weak ones and to give a class of submanifolds in symmetric spaces all of whose focal points (other than conjugate points) are strong ones. The third purpose is to construct examples of submanifolds in symmetric spaces admitting weak ones.