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 : 33. 47 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

Far East Journal Of Mathematical Sciences

Author :
ISBN : UOM:39015072701918
Genre : Mathematics
File Size : 71. 29 MB
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Modeling Of Curves And Surfaces With Matlab

Author : Vladimir Rovenski
ISBN : 9780387712772
Genre : Mathematics
File Size : 68. 92 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.

Knots And Physics Third Edition

Author : Kauffman
ISBN : 9812384839
Genre : Electronic books
File Size : 88. 9 MB
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This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.

Indra S Pearls

Author : David Mumford
ISBN : 0521352533
Genre : Mathematics
File Size : 54. 37 MB
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Highly illustrated realization of infinitely reflected images related to fractals, chaos and symmetry.

A Course In Metric Geometry

Author : Dmitri Burago
ISBN : 9780821872185
Genre : Mathematics
File Size : 70. 86 MB
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"Metric geometry" is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces).

Decorated Teichm Ller Theory

Author : R. C. Penner
ISBN : 3037190752
Genre : Mathematics
File Size : 25. 71 MB
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