geometry of mobius transformations elliptic parabolic and hyperbolic actions of sl2r

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Geometry Of M Bius Transformations

Author : Vladimir V Kisil
ISBN : 9781908977601
Genre : Mathematics
File Size : 77. 54 MB
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This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action. The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered. Sample Chapter(s) Chapter 1: Erlangen Programme: Preview (267 KB) Contents:Erlangen Programme: PreviewGroups and Homogeneous SpacesHomogeneous Spaces from the Group SL2(R)The Extended Fillmore–Springer–Cnops ConstructionIndefinite Product Space of CyclesJoint Invariants of Cycles: OrthogonalityMetric Invariants in Upper Half-PlanesGlobal Geometry of Upper Half-PlanesInvariant Metric and GeodesicsConformal Unit DiskUnitary Rotations Readership: Undergraduate and graduate students in geometry and algebra. Keywords:SL2(R);Elliptic;Parabolic;Hyperbolic;Complex Numbers;Dual Numbers;Double Numbers;Split-Complex Numbers;Möbius Transformations;Geometry;Hyperbola;Parabola;Circle;Symmetry;Group;Geodesics;Invariant;Orthogonality;Conic Sections;Distance;Length

Geometry Of M Bius Transformations

Author : Vladimir V. Kisil
ISBN : 9781848168589
Genre : Mathematics
File Size : 84. 68 MB
Format : PDF, ePub
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This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered.

Far East Journal Of Mathematical Sciences

Author :
ISBN : UOM:39015072701918
Genre : Mathematics
File Size : 75. 44 MB
Format : PDF
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The 1 2 3 Of Modular Forms

Author : Jan Hendrik Bruinier
ISBN : 3540741194
Genre : Mathematics
File Size : 41. 70 MB
Format : PDF
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This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Modeling Of Curves And Surfaces With Matlab

Author : Vladimir Rovenski
ISBN : 9780387712772
Genre : Mathematics
File Size : 29. 48 MB
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This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.

Indra S Pearls

Author : David Mumford
ISBN : 0521352533
Genre : Mathematics
File Size : 42. 17 MB
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Highly illustrated realization of infinitely reflected images related to fractals, chaos and symmetry.

Geometry Of Complex Numbers

Author : Hans Schwerdtfeger
ISBN : 0486638308
Genre : Mathematics
File Size : 58. 10 MB
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Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries. "This book should be in every library, and every expert in classical function theory should be familiar with this material. The author has performed a distinct service by making this material so conveniently accessible in a single book." — Mathematical Review.

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