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A characterization of Möbius transformations
Authors:Roland Hö  fer
Affiliation:Mathematisches Seminar, Universität Hamburg, Bundesstr. 55, 20146 Hamburg, Germany
Abstract:Let $nge 2$ be an integer and let $mathcal{D}$ be a domain of $mathbb{R}^n$. Let $f:mathcal{D}tomathbb{R}^n$ be an injective mapping which takes hyperspheres whose interior is contained in $mathcal{D}$ to hyperspheres in $mathbb{R}^n$. Then $f$ is the restriction of a Möbius transformation.

Keywords:M{"  o}bius transformation, Lie transformation, mappings preserving hyperspheres, Alexandrov's theorem for domains
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