Geodesic orbit Riemannian metrics on spheres

Nikonorov Yu. G.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 3.

Abstract:
In this paper, a complete classification of geodesic orbit Riemannian metrics on spheres \(S^n\) is obtained. We also construct some explicit examples of geodesic vectors for \(Sp(n+1)U(1)$\)-invariant metrics on \(S^{4n+3}\).

Keywords: homogeneous spaces, homogeneous Riemannian manifolds, naturally reductive Riemannian manifolds, normal homogeneous Riemannian manifolds, geodesic orbit spaces, symmetric spaces, weakly symmetric spaces

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