Totally geodesic immersions into Grassmannians (harmonic maps into Grassmann manifolds II)

Abstract

We define a totally geodesic immersion of irreducible type from a symmetric space of compact type into a Grassmannian and classify such immersions. Any totally geodesic immersion is related to a homogeneous vector bundle with the canonical connection and the eigenspaces of the Laplace operator acting on the space of sections of the bundle.