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

Abstract

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 ( n 1 ) × ⋯ × Sp ( n s ) , g ) , with 0 n 1 + ⋯ + n s ≤ 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.