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A characterization of Möbius transformations

Author: Roland Höfer
Journal: Proc. Amer. Math. Soc. 128 (2000), 1197-1201
MSC (1991): Primary 51B10; Secondary 51M04, 51M09
Published electronically: August 3, 1999
MathSciNet review: 1646191
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $n\ge 2$ be an integer and let $\mathcal{D}$ be a domain of $\mathbb{R}^n$. Let $f:\mathcal{D}\to\mathbb{R}^n$ 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.

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Additional Information

Roland Höfer
Affiliation: Mathematisches Seminar, Universität Hamburg, Bundesstr. 55, 20146 Hamburg, Germany

Keywords: M{\"o}bius transformation, Lie transformation, mappings preserving hyperspheres, Alexandrov's theorem for domains
Received by editor(s): June 4, 1998
Published electronically: August 3, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society