A Gyrovector Space Approach to Hyperbolic Geometry

DOI10.2200/S00175ED1V01Y200901MAS004zbMath1208.51014MaRDI QIDQ3585728

Abraham A. Ungar

Publication date: 2 September 2010

Published in: Synthesis Lectures on Mathematics and Statistics (Search for Journal in Brave)

zbMATH Keywords

plane hyperbolic geometrygyrogroupsgyrovectorgyrotrigonometryMöbius and Einstein gyrovector spaces

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry (51-01)

Related Items (8)

Geometry of gyrogroups via Klein's approach ⋮ The Algebra of Gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems ⋮ Novel Tools to Determine Hyperbolic Triangle Centers ⋮ A Mazur-Ulam theorem for normed gyrolinear spaces ⋮ The cogyrolines of Möbius gyrovector spaces are metric but not periodic ⋮ The Einstein relativistic velocity model of hyperbolic geometry and its plane separation axiom ⋮ Calculus of operators: covariant transform and relative convolutions ⋮ The three Steiner-Lehmus theorems

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