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
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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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