Geodesic orbit spaces of compact Lie groups of rank two
Differential Geometry
2020-10-09 v2
Abstract
Geodesic orbit spaces are those Riemannian homogeneous spaces (G/H,g) whose geodesics are orbits of one-parameter subgroups of G. We classify the simply connected geodesic orbit spaces where G is a compact Lie group of rank two. We prove that the only such spaces for which the metric g is not induced from a bi-invariant metric on G are certain spheres and projective spaces, endowed with metrics induced from Hopf fibrations.
Keywords
Cite
@article{arxiv.2008.13588,
title = {Geodesic orbit spaces of compact Lie groups of rank two},
author = {Nikolaos Panagiotis Souris},
journal= {arXiv preprint arXiv:2008.13588},
year = {2020}
}
Comments
14 pages, The omission of the Berger spheres in the main theorem is fixed