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Quaternionic linear fractional transformations and direct isometries of H5

Moussafir, Jacques-Olivier (2001), Quaternionic linear fractional transformations and direct isometries of H5, Journal of Geometry and Physics, 37, 3, p. 183-189. http://dx.doi.org/10.1016/S0393-0440(99)00052-2

Type
Article accepté pour publication ou publié
Date
2001
Journal name
Journal of Geometry and Physics
Volume
37
Number
3
Publisher
Elsevier
Pages
183-189
Publication identifier
Metadata
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Author(s)
Moussafir, Jacques-Olivier
Abstract (EN)
In the complex plane, an even number of reflection through lines or circles can be expressed in complex coordinates as a linear fractional transformation w=(az+b)/(cz+d) with Image and ad−bc≠0. This also holds in Image : an even number of reflections through spheres or planes correspond to transformations k=(ah+b)(ch+d)−1 with Image . A theorem by Poincaré about direct isometries of hyperbolic spaces may therefore be rephrased: direct isometries of H5 correspond to quaternionic linear fractional transformations.
Subjects / Keywords
Quaternions; Isometries; Transformations; Differential geometry