Geodesic orbit Riemannian spaces with two isotropy summands. I

Abstract

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. The main result is the classification of compact simply connected geodesic orbit Riemannian spaces $G/H$ with two irreducible submodules in the isotropy representation.

15 pages, comments are welcome

References in corpus (4)

• Compact Riemannian Manifolds with Homogeneous Geodesics
• On the structure of geodesic orbit Riemannian spaces
• On invariant Riemannian metrics on Ledger-Obata spaces
• Invariant Einstein metrics on Ledger-Obata spaces

Cited by in corpus (7)

• Compact geodesic orbit spaces with a simple isotropy group
• Spectral properties of Killing vector fields of constant length
• Einstein Lie groups, geodesic orbit manifolds and regular Lie subgroups
• On geodesic orbit nilmanifolds
• Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds
• Standard homogeneous $({\alpha }_1,{\alpha }_2)$-metrics and geodesic orbit property
• Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces