The hyperbolic derivative in the Poincaré ball model of hyperbolic geometry

DOI10.1006/JMAA.2000.7280zbMath0976.51009OpenAlexW2052639453MaRDI QIDQ5927731

Graciela Silvia Birman, Abraham A. Ungar

Publication date: 28 December 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/0d07b645f4fb108b643ccdda4cefaff0ec7f1410

zbMATH Keywords

ball of any real inner product spacegeneric Möbius transformationMöbius additiontheories of gyrogroups and gyrovector spaces

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Geodesics in global differential geometry (53C22) Loops, quasigroups (20N05)

Related Items (2)

Seeing the Möbius disc-transformation group like never before. ⋮ Einstein's velocity addition law and its hyperbolic geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The relativistic noncommutative nonassociative group of velocities and the Thomas rotation
• Hyperbolic trigonometry in the Einstein relativistic velocity model of hyperbolic geometry
• Extension of the unit disk gyrogroup into the unit ball of any real inner product space
• The Hyperbolic Pythagorean Theorem in the Poincare Disc Model of Hyperbolic Geometry
• A new characteristic of Möbius transformations by use of Apollonius quadrilaterals
• Hyperbolic trigonometry and its application in the Poincaré ball model of hyperbolic geometry

This page was built for publication: The hyperbolic derivative in the Poincaré ball model of hyperbolic geometry