Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A characterization of Möbius transformations

Author(s): Roland Höfer
Journal: Proc. Amer. Math. Soc. 128 (2000), 1197-1201.
MSC (1991): Primary 51B10; Secondary 51M04, 51M09
Posted: August 3, 1999
MathSciNet review: 1646191
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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 is the restriction of a Möbius transformation.

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