English

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