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Homogeneous spaces with geodesic orbit Riemannian metrics and with integrable invariant distributions
We consider two types of homogeneous spaces of Lie groups with compact stabilizer subgroups: those with integrable invariant distributions and those for which all invariant Riemannian metrics are geodesic orbit. Recall that a Riemannian metric is called geodesic orbit if each geodesic is an orbit of
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