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Hyperbolic Geometry

Posted By: AvaxGenius
Hyperbolic Geometry

Hyperbolic Geometry by James W. Anderson
English | PDF | 1999 | 239 Pages | ISBN : 1852331569 | 18.15 MB

The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.

Lectures on Hyperbolic Geometry

Posted By: AvaxGenius
Lectures on Hyperbolic Geometry

Lectures on Hyperbolic Geometry by Riccardo Benedetti , Carlo Petronio
English | PDF | 1992 | 343 Pages | ISBN : 354055534X | 28.07 MB

In recent years hyperbolic geometry has been the object and the preparation for extensive study that has produced important and often amazing results and also opened up new questions. The book concerns the geometry of manifolds and in particular hyperbolic manifolds; its aim is to provide an exposition of some fundamental results, and to be as far as possible self-contained, complete, detailed and unified. Since it starts from the basics and it reaches recent developments of the theory, the book is mainly addressed to graduate-level students approaching research, but it will also be a helpful and ready-to-use tool to the mature researcher. After collecting some classical material about the geometry of the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (of which a complete proof is given following Gromov and Thurston) and Margulis' lemma. These results form the basis for the study of the space of the hyperbolic manifolds in all dimensions (Chabauty and geometric topology); a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory.

Geometry II: Spaces of Constant Curvature

Posted By: AvaxGenius
Geometry II: Spaces of Constant Curvature

Geometry II: Spaces of Constant Curvature by E. B. Vinberg
English | PDF | 1993 | 263 Pages | ISBN : 3540520007 | 24 MB

Spaces of constant curvature, i.e. Euclidean space, the sphere, and Loba­ chevskij space, occupy a special place in geometry. They are most accessible to our geometric intuition, making it possible to develop elementary geometry in a way very similar to that used to create the geometry we learned at school. However, since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space, the original source of our geometric intuition. Euclidean geometry has for a long time been deeply rooted in the human mind. The same is true of spherical geometry, since a sphere can naturally be embedded into a Euclidean space.

Geometric and Ergodic Aspects of Group Actions (Repost)

Posted By: AvaxGenius
Geometric and Ergodic Aspects of Group Actions (Repost)

Geometric and Ergodic Aspects of Group Actions by S. G. Dani
English | PDF | 2019 | 176 Pages | ISBN : 9811506825 | 5.3 MB

This book gathers papers on recent advances in the ergodic theory of group actions on homogeneous spaces and on geometrically finite hyperbolic manifolds presented at the workshop “Geometric and Ergodic Aspects of Group Actions,” organized by the Tata Institute of Fundamental Research, Mumbai, India, in 2018. Written by eminent scientists, and providing clear, detailed accounts of various topics at the interface of ergodic theory, the theory of homogeneous dynamics, and the geometry of hyperbolic surfaces, the book is a valuable resource for researchers and advanced graduate students in mathematics.