Analytic Hyperbolic Geometry: Mathematical Foundations And Applications

Szerző: Abraham A. Ungar

Nyelv:

Kötés: Kemény kötésű

Kiadó: World Scientific Publishing Co Pte Ltd

Elérhetőség: 50 % esély

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This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geomet...

Információk a könyvről

Szerző

Abraham A. Ungar

Nyelv

Angol

Kötés

Könyv - Kemény kötésű

Kiadva

2005

oldal

484

EAN

9789812564573

ISBN

9812564578

Enbook ID

05068129

Kiadó

World Scientific Publishing Co Pte Ltd

Súly

806

Méretek

156 x 232 x 30

Teljes leírás

This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. In the resulting "gyrolanguage" of the book, one attaches the prefix "gyro" to a classical term to mean the analogous term in hyperbolic geometry. The book begins with the definition of gyrogroups, which is fully analogous to the definition of groups. Gyrogroups, both gyrocommutative and nongyrocommutative, abound in group theory. Surprisingly, the seemingly structureless Einstein velocity addition of special relativity turns out to be a gyrocommutative gyrogroup operation. Introducing scalar multiplication, some gyrocommutative gyrogroups of gyrovectors become gyrovector spaces. The latter, in turn, form the setting for analytic hyperbolic geometry just as vector spaces form the setting for analytic Euclidean geometry. By hybrid techniques of differential geometry and gyrovector spaces, it is shown that Einstein (Mobius) gyrovector spaces form the setting for Beltrami-Klein (Poincare) ball models of hyperbolic geometry. Finally, novel applications of Mobius gyrovector spaces in quantum computation, and of Einstein gyrovector spaces in special relativity, are presented.

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Analytic Hyperbolic Geometry: Mathematical Foundations And Applications

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