Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL2[subscript 2](R)[real number]
- Vladimir V. Kisil.
- London : Imperial College Press ; Singapore : Distributed by World Scientific, c2012.
- Physical description
- xiv, 192 p. : ill. ; 24 cm. + 1 DVD-ROM (4 3/4 in.)
Math & Statistics Library
Library has: 1 v. + 1 DVD-
|QA601 .K57 2012||Unknown|
- Kisil, Vladimir V.
- Includes bibliographical references (p. 173-179) and index.
- Erlangen Programme: Introduction-- Groups and Homogeneous Spaces-- Homogeneous Spaces from the Group SL(2, R)-- Fillmore - Springer - Cnops Construction-- Metric Invariants in Upper Half-Planes-- Global Geometry of Upper Half-Planes-- Conformal Unit Disk-- Geodesics-- Unitary Rotations.
- (source: Nielsen Book Data)
- Publisher's Summary
- This book is a unique exposition of rich and inspiring geometries associated with Mobius 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 Mobius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers. They form three possible commutative associative two-dimensional algebras, which are in perfect correspondences with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered.
(source: Nielsen Book Data)
- Publication date
- Title Variation
- Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL2(R)
- DVD-ROM contains illustrations, software, documentation in .pdf format, etc.
- 9781848168589 (hbk.)
- 1848168586 (hbk.)
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