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 (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 H1 × • • • × Hs, where Hj is of the same type as G. This class includes spheres, Stiefel manifolds, Grassmann manifolds and r… Show more
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