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 $$(M=G/H,g)$$ whose geodesics orbits of one-parameter subgroups G. The corresponding metric g is called a geodesic metric. We study the form (G/H, g), such that G one compact classical Lie groups $${{\,\mathrm{SO}\,}}(n)$$ , $$\mathrm{U}(n)$$ and H diagonally embedded product $$H_1\times \cdots \times H_s$$ where $$H_j$$ same type This class includes spheres, Stiefel manifolds, Grassmann manifolds real flag manifolds. present work contribution to g) with semisimple.