Geodesic Orbit Riemannian Structures on ${\mathbf{R}}^n$

Abstract

A geodesic orbit manifold is a complete Riemannian manifold all of whose geodesics are orbits of one-parameter groups of isometries. We give both a geometric and an algebraic characterization of geodesic orbit manifolds that are diffeomorphic to ${\mathbf{R}}^n$. Along the way, we establish various structural properties of more general geodesic orbit manifolds.

12 pages

References in corpus (3)

• Compact Riemannian Manifolds with Homogeneous Geodesics
• On the structure of geodesic orbit Riemannian spaces
• Generalized normal homogeneous Riemannian metrics on spheres and projective spaces

Cited by in corpus (7)

• Geodesic orbit metrics in a class of homogeneous bundles over quaternionic Stiefel manifolds
• Spectral properties of Killing vector fields of constant length
• On geodesic orbit nilmanifolds
• Geodesic orbit Finsler metrics on Euclidean spaces
• 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 Finsler space with $K\ge 0$ and the (FP) condition