Lobachevsky Geometry and Modern Nonlinear Problems

Authors: Popov, Andrey

  • First summary of research in the field of applications of hyperbolic geometry to solve theoretical physics problems
  • Clearly written and well presented
  • Provides an extensive list of relevant literature
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Hardcover $129.00
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  • Due: August 31, 2016
  • ISBN 978-3-319-34622-9
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About this book

This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years. The central sections cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives, and their applications to the analysis of the physical models. As the sine-Gordon equation appears to have profound “geometrical roots” and numerous applications to modern nonlinear problems, it is treated as a universal “object” of investigation, connecting many of the problems discussed.

The aim of this book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the context of non-Euclidean hyperbolic geometry.

Reviews

“The main aim of this book is to look at the potential of the geometry developed by Lobachevskii in the context of its emergence in various branches of current interest in contemporary mathematics and science, especially in nonlinear problems of mathematical physics. … the book is well written, very readable, and nicely illustrated throughout with many graphs and figures, especially figures of surfaces. … This unique book makes this difficult subject interesting and within reach.” (Paul F. Bracken, Mathematical Reviews, August, 2015)

“The book is original in its form and content. It covers a wide spectrum of geometry and analysis and it displays the Lobachevsky plane as a central object in the study of the classical equations of mathematical physics. The style is expository and clear. This book is a valuable addition to the geometric literature.” (Athanase Papadopoulos, zbMATH 1311.51002, 2015)


Table of contents (6 chapters)

  • Introduction

    Popov, Andrey

    Pages 1-14

  • Foundations of Lobachevsky geometry: axiomatics, models, images in Euclidean space

    Popov, Andrey

    Pages 15-59

  • The problem of realizing the Lobachevsky geometry in Euclidean space

    Popov, Andrey

    Pages 61-126

  • The sine-Gordon equation: its geometry and applications of current interest

    Popov, Andrey

    Pages 127-223

  • Lobachevsky geometry and nonlinear equations of mathematical physics

    Popov, Andrey

    Pages 225-257

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-05669-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-05668-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: August 31, 2016
  • ISBN 978-3-319-34622-9
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lobachevsky Geometry and Modern Nonlinear Problems
Authors
Translated by
Iacob, A.
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-05669-2
DOI
10.1007/978-3-319-05669-2
Hardcover ISBN
978-3-319-05668-5
Softcover ISBN
978-3-319-34622-9
Edition Number
1
Number of Pages
VIII, 310
Number of Illustrations and Tables
103 b/w illustrations
Additional Information
Original Russian edition published by the Publishing House of Physical Department of Lomonosov Moscow State University, Moscow, 2012
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