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 \(d_{{\mathfrak H}}\).
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Communicated by A. Constantin.
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Platis, I.D., Schroeder, V. Möbius rigidity of invariant metrics in boundaries of symmetric spaces of rank-1. Monatsh Math 183, 357–373 (2017). https://doi.org/10.1007/s00605-016-0982-1
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DOI: https://doi.org/10.1007/s00605-016-0982-1