Geodesic orbit metrics in a class of homogeneous bundles over quaternionic Stiefel manifolds

Abstract

Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces (M = G/H, g) whose geodesics are orbits of one-parameter subgroups of G. The corresponding metric g is called a geodesic orbit metric. We study the geodesic orbit spaces of the form (Sp(nSuch spaces include spheres, quaternionic Stiefel manifolds, Grassmann manifolds and quaternionic flag manifolds. The present work is a contribution to the study of g.o. spaces (G/H, g) with H semisimple.