Analytic Hyperbolic Geometry: Mathematical Foundations And Applications

Autor: Abraham A. Ungar

Jazyk:

Väzba: Pevná

Vydavateľ: World Scientific Publishing Co Pte Ltd

Dostupnosť: 50 % šanca

Prehľadáme celý svet

180.05 €

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

Informácie o knihe

Autor

Abraham A. Ungar

Jazyk

Angličtina

Väzba

Kniha - Pevná

Vydalo

2005

Stránok

484

EAN

9789812564573

ISBN

9812564578

Enbook ID

05068129

Vydavateľ

World Scientific Publishing Co Pte Ltd

Hmotnosť

806

Rozmery

156 x 232 x 30

Kompletný popis

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.

Mohlo by vás zaujímať

Zákazníci, ktorí si kúpili túto knihu, kúpili tiež

Najčastejšie vyhľadávané

Categories

Authors

Publishers

Produkty

Produkty

Najčastejšie vyhľadávané

Categories

Authors

Publishers

Produkty

Produkty

Analytic Hyperbolic Geometry: Mathematical Foundations And Applications

Informácie o knihe

Kompletný popis

Mohlo by vás zaujímať

Zákazníci, ktorí si kúpili túto knihu, kúpili tiež