Isometry groups of Alexandrov spaces
Differential Geometry
2014-02-26 v3
Abstract
For an Alexandrov space (with curvature bounded below), we determine the maximal dimension of its isometry group and show that the space is isometric to a Riemannian manifold, provided the dimension of its isometry group is maximal. We also determine a gap in the possible dimensions of the isometry groups and show that if the Alexandrov space is symmetric, then it is isometric to a Riemannian manifold.
Keywords
Cite
@article{arxiv.1109.4878,
title = {Isometry groups of Alexandrov spaces},
author = {Fernando Galaz-Garcia and Luis Guijarro},
journal= {arXiv preprint arXiv:1109.4878},
year = {2014}
}
Comments
Final version of the paper, accepted for publication at the Bulletin of the London Mathematical Society. It improves the proof of the Principal Orbit Theorem in section 2, and completes the missing cases in section 6 on dimension gaps