Homogeneity rank and atoms of actions
Two interesting concepts for smooth actions of compact Lie groups on manifolds are introduced in this well written paper. The notion of homogeneity rank is a numerical invariant of such an action. For isometric actions on compact Riemannian manifolds with positive sectional curvature the precise range of this invariant is determined. Special properties of actions with maximal homogeneity rank are studied. The notion of atoms is introduced as special components of the fixed point sets inheriting many properties of the original action. In some cases the atoms are determined.
scientific article; zbMATH DE number 1880575