Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL2[subscript 2](R)[real number]
 Responsibility
 Vladimir V. Kisil.
 Language
 English.
 Imprint
 London : Imperial College Press ; Singapore : Distributed by World Scientific, c2012.
 Physical description
 xiv, 192 p. : ill. ; 24 cm. + 1 DVDROM (4 3/4 in.)
Access
Available online
 www.worldscientific.com World Scientific
 ebrary
Math & Statistics Library
Stacks
Library has: 1 v. + 1 DVDROM
Call number  Status 

QA601 .K57 2012  Unknown 
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Creators/Contributors
 Author/Creator
 Kisil, Vladimir V.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 173179) and index.
 Contents

 Erlangen Programme: Introduction Groups and Homogeneous Spaces Homogeneous Spaces from the Group SL(2, R) Fillmore  Springer  Cnops Construction Metric Invariants in Upper HalfPlanes Global Geometry of Upper HalfPlanes 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 selfcontained 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 twodimensional algebras, which are in perfect correspondences with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean spacetime are considered.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Title Variation
 Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL2(R)
 Note
 DVDROM contains illustrations, software, documentation in .pdf format, etc.
 ISBN
 9781848168589 (hbk.)
 1848168586 (hbk.)