On left-invariant Einstein Riemannian metrics that are not geodesic orbit

Abstract

In this paper we prove that the compact Lie group $G_2$ admits a left-invariant Einstein metric that is not geodesic orbit. In order to prove the required assertion, we develop some special tools for geodesic orbit Riemannian manifolds. It should be noted that a suitable metric is discovered in a recent paper by I. Chrysikos and Y. Sakane, where the authors proved also that this metric is not naturally reductive.

16 pages, small corrections, comments are welcome

References in corpus (4)

• Compact Riemannian Manifolds with Homogeneous Geodesics
• On the structure of geodesic orbit Riemannian spaces
• Non-naturally reductive Einstein metrics on exceptional Lie groups
• Einstein Metrics from Symmetry and Bundle Constructions: A Sequel

Cited by in corpus (4)

• Einstein Lie groups, geodesic orbit manifolds and regular Lie subgroups
• Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces
• Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds
• Geodesic Orbit Metrics on Compact Simple Lie Groups arising from Generalized Flag Manifolds