The volume of geodesic balls and tubes about totally geodesic submanifolds in compact symmetric spaces (Q1360097)

Let \((M,g)\) be a compact Riemannian symmetric space. Using root systems, the authors derive explicit expressions for the volumes of geodesic spheres, balls and tubes about the compact totally geodesic submanifolds \(P\) such that the reflections in \(P\) are isometries. They also plot some of these volume functions for a selection of particular compact irreducible Riemannian symmetric spaces of rank two.