A characterization of Möbius transformations

Höfer, Roland

doi:10.1090/S0002-9939-99-05203-X

A characterization of Möbius transformations
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by Roland Höfer PDF

Proc. Amer. Math. Soc. 128 (2000), 1197-1201 Request permission

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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