On a class of geodesic orbit spaces with abelian isotropy subgroup. (English) Zbl 1478.53095

Souris, Nikolaos Panagiotis

Manuscr. Math. 166, No. 1-2, 101-129 (2021).

We say that a Riemannian manifold \((M,g)\) is a geodesic orbit (g.o) manifold if any geodesic of \(M\) is an orbit of a one-parameter subgroup of the entire isometry group of \(M\). The author considers g.o. spaces of the form \((G/S, g)\) such that \(G\) is a compact, connected, semisimple Lie group and the isotropy subgroup \(S\) is abelian. He states (Theorem 1.1) that \(G/S\) is a g.o space if and only if \(g\) is a \(G\)-naturally reductive metric, i.e., a suitable \(G\)-invariant metric (resp., an induced from a bi-invariant Riemannian metric on \(G\)).

Reviewer: Mohammed El Aïdi (Bogotá)

MSC:

53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30	Differential geometry of homogeneous manifolds

Keywords:

Homogeneous spaces: isotropy subgroup; semisimple Lie group

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