Abstract
The theory of Möbius transformations in ℝn can be treated in various ways. One way is to use the projective model of hyperbolic geometry which expresses the Möbius transformations in terms of the matrix group O(n + 1,1). While very satisfactory from a theoretical point of view it leads quickly to overly complicated formulas, and I have therefore advocated an approach which works directly in ℝn and uses formulas strikingly analogous to those in the complex case [1].
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References
Ahlfors, L. V.: Möbius transformations in several dimensions. Lecture Notes, University of Minnesota (1981)
Clifford, W. K.: Mathematical Papers. Macmillan, London (1882)
Fueter, R.: Sur les groupes improprement discontinus. Comptes Rendus Acad. des Sciences, 182 (1926)
Fueter, R.: Über automorphe Funktionen in bezug auf Gruppen, die in der Ebene uneigentlich diskontinuierlich sind. Crelle Journal 157 (1927)
Lounesto, P., Latvamaa, E.: Conformai transformations and Clifford numbers. Proc. Am. Math. Soc. 79, 4 (1980)
Maass, H.: Automorphe Funktionen von mehreren Veränderlichen und Dirichletsche Reihen. Hamburg Abh. 16 (1949)
Porteous, I. R.: Topological Geometry. Cambridge University Press, 2nd ed. (1981)
Vahlen, K. Th.: Über Bewegungen und komplexe Zahlen. Math. Annalen 55 (1902)
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© 1985 Springer-Verlag Berlin, Heidelberg
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Ahlfors, L.V. (1985). Möbius Transformations and Clifford Numbers. In: Chavel, I., Farkas, H.M. (eds) Differential Geometry and Complex Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69828-6_5
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DOI: https://doi.org/10.1007/978-3-642-69828-6_5
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