Mathematics – Differential Geometry
Scientific paper
2009-12-04
Mathematische Annalen 347, 4 (2010) 951-961
Mathematics
Differential Geometry
13 pages, to appear in Mathematische Annalen
Scientific paper
10.1007/s00208-009-0464-z
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.
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