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Monatshefte für Mathematik

, Volume 183, Issue 2, pp 357–373 | Cite as

Möbius rigidity of invariant metrics in boundaries of symmetric spaces of rank-1

  • I. D. PlatisEmail author
  • V. Schroeder
Article

Abstract

Let \({\mathbf{H}}^n_{{\mathbb K}}\) denote the symmetric space of rank-1 and of non-compact type and let \(d_{{\mathfrak H}}\) be the Korányi metric defined on its boundary. We prove that if d is a metric on \(\partial {\mathbf{H}}^n_{{\mathbb K}}\) such that all Heisenberg similarities are d-Möbius maps, then under a topological condition d is a constant multiple of a power of \(d_{{\mathfrak H}}\).

Keywords

Möbius space Invariant metric Boundary of symmetric space 

Mathematics Subject Classification

51B10 51F99 

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Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Applied MathematicsUniversity of Crete, University CampusHeraklion, CreteGreece
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland

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