Convexity of Reflective Submanifolds in Special Unitary Groups

Abstract

A submanifold of a Riemannian manifold is called reflective, if it is a connected component of an involutive isometry. If every shortest geodesic arc of a complete submanifold is still shortest in the ambient space, we say that the submanifold is convex. In this note we show that reflective submanifolds in special unitary groups are convex.