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arXiv · 1406.6770

Moebius rigidity of invariant metrics in boundaries of symmetric spaces of rank 1

I. D. Platis·V. Schroeder
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Abstract

Let $\partial{\bf H}^n_{\mathbb K}$ denote the boundary of a symmetric space of rank-one and of non-compact type and let $d_{\mathfrak{H}}$ be the Kor\'anyi metric defined in $\partial{\bf H}^n_{\mathbb K}$. We prove that if $d$ is a metric on $\partial{\bf H}^n_{\mathbb K}$ such that all Heisenberg similarities are $d$-M\"obius maps, then under a topological condition $d$ is a constant multiple of a power of $d_{\mathfrak{H}}$.

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I. D. Platis, V. Schroeder. 2014-06-26. Moebius rigidity of invariant metrics in boundaries of symmetric spaces of rank 1. https://arxiv.org/abs/1406.6770

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