Author : John Stillwell
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 29,56 MB
Release : 1996
Category : Mathematics
ISBN : 9780821809228
Presents the papers of Beltrami, Klein, and Poincare that brought hyperbolic geometry into the mainstream of mathematics.
Author : Jacques Hadamard
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 12,43 MB
Release : 1999-01-01
Category : Mathematics
ISBN : 9780821890479
This is the English translation of a volume originally published only in Russian and now out of print. The book was written by Jacques Hadamard on the work of Poincare. Poincare's creation of a theory of automorphic functions in the early 1880s was one of the most significant mathematical achievements of the nineteenth century. It directly inspired the uniformization theorem, led to a class of functions adequate to solve all linear ordinary differential equations, and focused attention on a large new class of discrete groups. It was the first significant application of non-Euclidean geometry. This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts.
Author : Riccardo Benedetti
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 37,11 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642581587
Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as self-contained, complete, detailed and unified as possible. Following some classical material on the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (including a complete proof, following Gromov and Thurston) and Margulis' lemma. These then form the basis for studying Chabauty and geometric topology; a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory; and much space is devoted to the 3D case: a complete and elementary proof of the hyperbolic surgery theorem, based on the representation of three manifolds as glued ideal tetrahedra.
Author : Michael P. Hitchman
Publisher : Jones & Bartlett Learning
Page : 255 pages
File Size : 45,56 MB
Release : 2009
Category : Mathematics
ISBN : 0763754579
The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.
Author : Daina Taimina
Publisher : CRC Press
Page : 865 pages
File Size : 12,53 MB
Release : 2018-02-19
Category : Mathematics
ISBN : 1351402196
Winner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.
Author : R. D. Canary
Publisher : Cambridge University Press
Page : 356 pages
File Size : 22,99 MB
Release : 2006-04-13
Category : Mathematics
ISBN : 9781139447195
Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.
Author : Silvio Levy
Publisher : Cambridge University Press
Page : 212 pages
File Size : 28,92 MB
Release : 1997-09-28
Category : Mathematics
ISBN : 9780521629621
Flavors of Geometry is a volume of lectures on four geometrically-influenced fields of mathematics that have experienced great development in recent years. Growing out of a series of introductory lectures given at the Mathematical Sciences Research Institute in January 1995 and January 1996, the book presents chapters by masters in their respective fields on hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation. Each lecture begins with a discussion of elementary concepts, examines the highlights of the field, and concludes with a look at more advanced material. The style and presentation of the chapters are clear and accessible, and most of the lectures are richly illustrated. Bibiliographies and indexes are included to encourage further reading on the topics discussed.
Author : Birger Iversen
Publisher : Cambridge University Press
Page : 317 pages
File Size : 21,24 MB
Release : 1992-12-17
Category : Mathematics
ISBN : 0521435080
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.
Author : James W. Anderson
Publisher : Springer Science & Business Media
Page : 239 pages
File Size : 45,29 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 1447139879
Thoroughly updated, featuring new material on important topics such as hyperbolic geometry in higher dimensions and generalizations of hyperbolicity Includes full solutions for all exercises Successful first edition sold over 800 copies in North America
Author : Jessica S. Purcell
Publisher : American Mathematical Soc.
Page : 369 pages
File Size : 22,75 MB
Release : 2020-10-06
Category : Education
ISBN : 1470454998
This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.
