Minimal orbits of the isotropy groups of symmetric spaces of compact type

Abstract

Let M be a compact symmetric space, and K the isotropy subgroup of the group of all isometries of M at a point o of M . We consider two actions of K , namely the natural action of K on M and the linear isotropy action of K on the tangent space T o M . In both cases, we show that in each category of orbits of the “same type” under K there exists a unique minimal one.