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(n)∕Sp(n1)×⋯×Sp(ns),g), with 0<n1+⋯+ns≤n. Such 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. © 2021 Elsevier B.V.