A metric proof that -homogeneous manifolds are geodesic orbit manifolds
Volume 165 / 2021
Colloquium Mathematicum 165 (2021), 219-224
MSC: Primary 53C25; Secondary 53C30.
DOI: 10.4064/cm8222-7-2020
Published online: 21 December 2020
Abstract
A Riemannian manifold (M,g) is called \delta -homogeneous if for any pair of points p,q\in M there is an isometry f such that f(p)=q, and such that the points p,q have maximal displacement among all pairs x,f(x) with respect to the Riemannian distance. A result of V. N. Berestovskiĭ and Yu. G. Nikonorov states that any \delta -homogeneous manifold (M,g) is a geodesic orbit manifold, i.e. all geodesics in (M,g) are orbits of one-parameter subgroups of isometries. In this paper we give a simple proof of this result, based on a recent metric characterization of geodesics that are orbits.
