A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
By B. Leeb. 2009
84 citations recorded by the source corpus.
We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesics in X do not branch and a Euclidean building otherwise. Furthermore, every boundary equivalence (cone topology homeomorphism preserving the Tits metric) between two such spaces is induced by a homothety. As an application, we can extend the Mostow and Prasad rigidity theorems to com- pact singular (orbi)spaces of nonpositive curvature which are homotopy equivalent to a quotient of a symmetric space or Euclidean building by a cocompact group of isometries.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2dfedb87f47db46c8be58b3ae9ad4714c33f3450
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Anosov subgroups: dynamical and geometric characterizations (2017, background): “For more detailed discussions, we refer the reader to [2,7,23] and [26].”
- Isometry groups of non‐positively curved spaces: structure theory (2008, background): “Thus, if this building has non-zero dimension, we conclude from the main result of [43] that X is a Euclidean building of higher rank.”
- Dynamics on flag manifolds: domains of proper discontinuity and cocompactness (2013, methodology): “In this section, we collect some standard material on Coxeter complexes, the geometry of nonpositively curved symmetric spaces and associated spherical Tits buildings; we refer the reader to [26; 29] for more detailed discussion of symmetric spaces and buildings.”