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

TL;DR

This paper characterizes geodesic orbit Riemannian manifolds diffeomorphic to ^n, providing geometric and algebraic insights into their structure and properties.

Contribution

It offers the first comprehensive geometric and algebraic characterization of geodesic orbit manifolds on ^n, expanding understanding of their structure.

Findings

Characterization of geodesic orbit manifolds on ^n

Structural properties of general geodesic orbit manifolds

Algebraic and geometric criteria for such manifolds

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.