Fried's theorem for boundary geometries of rank one symmetric spaces

2019/09/24 by Raphaël V Alexandre, Alexandre, Raphaël
Mathematics · Computer Science · #Geometric and Algebraic Topology #Finite Group Theory Research #Computational Geometry and Mesh Generation

paper · pdf · doi:10.48550/arxiv.1909.10849

Abstract

After introducing the different boundary geometries of rank one symmetric spaces, we state and prove Fried's theorem in the general setting of all those geometries: a closed manifold with a similarity structure is either complete or the developing map is a covering onto the Heisenberg-type space deprived of a point.

Related

• Rank one symmetric spaces and Rigidity
• Geodesic convexity and closed nilpotent similarity manifolds
• A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
• Existence of non-isotropic conjugate points on rank one normal homogeneous spaces
• A characterization of higher rank symmetric spaces via bounded cohomology