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A Gyrovector Space Approach to Hyperbolic GeometryGyrovector Spaces

A Gyrovector Space Approach to Hyperbolic Geometry: Gyrovector Spaces [Some gyrocommutative gyrogroups admit scalar multiplication, giving rise to gyrovector spaces. The latter, in turn, are analogous to vector spaces just as gyrogroups are analogous to groups and gyrocommutative gyrogroups are analogous to commutative groups. Indeed, we will find in this book that gyrovector spaces provide the algebraic setting for hyperbolic geometry just as vector spaces provide the algebraic setting for Euclidean geometry.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Gyrovector Space Approach to Hyperbolic GeometryGyrovector Spaces

Part of the Synthesis Lectures on Mathematics & Statistics Book Series
Ungar, Abraham Albert
Springer Journals — Jan 1, 2009
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55 pages

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2009
ISBN
978-3-031-01268-6
Pages
55 –110
DOI
10.1007/978-3-031-02396-5_3
Publisher site
See Chapter on Publisher Site

Abstract

[Some gyrocommutative gyrogroups admit scalar multiplication, giving rise to gyrovector spaces. The latter, in turn, are analogous to vector spaces just as gyrogroups are analogous to groups and gyrocommutative gyrogroups are analogous to commutative groups. Indeed, we will find in this book that gyrovector spaces provide the algebraic setting for hyperbolic geometry just as vector spaces provide the algebraic setting for Euclidean geometry.]

Published: Jan 1, 2009

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