Geometry of Mobius Transformations: Elliptic, Parabolic and Hyperbolic Actions of Sl2(r) (with DVD-Rom)
Vladimir V Kisil
Gebundenes Buch

Geometry of Mobius Transformations: Elliptic, Parabolic and Hyperbolic Actions of Sl2(r) (with DVD-Rom)

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This book is a unique exposition of rich and inspiring geometries associated with M bius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL(2, R). Starting from elementary facts in group theory, the author unveiled surprising new results about geometry of circles, parabolas and hyperbolas, with the approach based on the Erlangen program of F Klein who defined geometry as a study of invariants under a transitive group action. The treatment of elliptic, parabolic and hyperbolic M bius transformations is provided in...