Isometry groups of Alexandrov spaces

Details Isometry groups of Alexandrov spaces Isometry groups of Alexandrov spaces

2011-09-22

arxiv.org/abs/1109.4878v2

Mathematics

Differential Geometry

The revised version contains a proof of the principal orbit theorem for isometric actions on Alexandrov spaces, as well as new

Scientific paper

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.

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