A new proof of the nonexistence of isometries between higher dimensional Euclidean and hyperbolic spaces

DOI10.1007/S00010-014-0316-0zbMath1336.51011OpenAlexW1996645038MaRDI QIDQ5964966

Oğuzhan Demirel

Publication date: 2 March 2016

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

Full work available at URL: https://doi.org/10.1007/s00010-014-0316-0

zbMATH Keywords

metric spacesEuclidean and non-Euclidean geometriesgyroalgebrametric hyperplanes

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Length, area and volume in real or complex geometry (51M25) Euclidean geometries (general) and generalizations (51M05)

Cites Work

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• Metric and periodic lines in real inner product space geometries
• The cogyrolines of Möbius gyrovector spaces are metric but not periodic
• Metric and periodic lines in the Poincaré ball model of hyperbolic geometry
• The hyperbolic square and Möbius transformations
• Einstein's velocity addition law and its hyperbolic geometry
• Metric lines in Lorentz--Minkowski geometry
• From Möbius to Gyrogroups
• An Introduction to Hyperbolic Barycentric Coordinates and their Applications
• Hyperbolic trigonometry and its application in the Poincaré ball model of hyperbolic geometry

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