Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds

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 ( G / H , g ), such that G is one of the compact classical Lie groups SO ( n ) , U ( n ) , and H is a diagonally embedded product H 1 × ⋯ × H s , where H j is of the same type as G . This class includes spheres, Stiefel manifolds, Grassmann manifolds and real flag manifolds. The present work is a contribution to the study of g.o. spaces ( G / H , g ) with H semisimple.