Symmetric spaces of higher rank do not admit differentiable compactifications
Abstract
Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or quaternionic CR depending of the space). One can ask whether such a differentiable compactification exists for higher rank spaces, hopefully leading to some knew geometry to explore. In this paper we answer negatively.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2009
- DOI:
- 10.48550/arXiv.0912.0814
- arXiv:
- arXiv:0912.0814
- Bibcode:
- 2009arXiv0912.0814K
- Keywords:
-
- Mathematics - Differential Geometry;
- 53C35;
- 57S20
- E-Print:
- 13 pages, to appear in Mathematische Annalen