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Zbl 0793.15019
Waterman, P.L.
Möbius transformations in several dimensions.
(English)
[J] Adv. Math. 101, No.1, 87-113 (1993). ISSN 0001-8708

From the author's introduction: {\it L. V. Ahlfors} [Differential Geometry and Complex Analysis, 65-73 (1985; Zbl 0569.30040)] shows how a $2\times 2$-matrix with entries in a Clifford algebra may be used to describe a Möbius transformation of $\bbfR\sp n\cup\{\infty\}$.\par We give a different development of Clifford matrices and discuss their relationship to hyperbolic isometries. A discreteness condition generalizing Jørgensen's inequality is then obtained and utilized to describe the nature of parabolic fixed points in higher dimensions. Although they cannot be conical limit points, we give an example to show that they may be horospherical limit points.
[A.Helversen-Pasotto (Nice)]
MSC 2000:
*15A66 Clifford algebras
53C56 Other complex differential geometry

Keywords: Clifford algebra; Möbius transformation; Clifford matrices; hyperbolic isometries; Jørgensen's inequality; parabolic fixed points; horospherical limit points

Citations: Zbl 0569.30040

Cited in: Zbl 1021.37025 Zbl 0965.15021

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