The cogyrolines of Möbius gyrovector spaces are metric but not periodic

DOI10.1007/S00010-012-0134-1zbMath1269.39007OpenAlexW2055203992MaRDI QIDQ1941994

Emine Soytürk Seyrantepe, Oğuzhan Demirel

Publication date: 25 March 2013

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-012-0134-1

zbMATH Keywords

metric spacequartic functional equationMöbius gyrovector spacedistance spacefunctional equations of metric and periodic lines and their solutionsPoincaré ball model of hyperbolic geometry

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Metric spaces, metrizability (54E35) Length, area and volume in real or complex geometry (51M25) Euclidean geometries (general) and generalizations (51M05) Möbius geometries (51B10) Matrix and operator functional equations (39B42)

Related Items (3)

The Algebra of Gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems ⋮ A new proof of the nonexistence of isometries between higher dimensional Euclidean and hyperbolic spaces ⋮ Gyrogroup actions: a generalization of group actions

Cites Work

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• Periodic lines in Lorentz-Minkowski geometry
• Metric and periodic lines in de Sitter's world
• Metric and periodic lines in real inner product space geometries
• Metric and periodic lines in the Poincaré ball model of hyperbolic geometry
• Metric lines in Lorentz--Minkowski geometry
• A Gyrovector Space Approach to Hyperbolic Geometry
• Beyond the Einstein addition law and its gyroscopic Thomas precession. The theory of gyrogroups and gyrovector spaces
• Hyperbolic trigonometry and its application in the Poincaré ball model of hyperbolic geometry

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