Möbius Transformation and Einsten Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky

2013/03/19 by Abraham A. Ungar, Ungar, Abraham A. · 1 citation
Engineering · Mathematics · Medicine · Physics and Astronomy · #83A05 51M10 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematics and Applications #Medical and Biological Sciences #math-ph #math.MP #msc:51M10 #msc:83A05

paper · pdf · doi:10.48550/arxiv.1303.4785

arXiv admin note: substantial text overlap with arXiv:1302.6961

arxiv created 2013/03/19 · openalex publication_date 2013/03/19 · arxiv updated 2013/03/21 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

In this chapter, dedicated to the 60th Anniversary of Themistocles M. Rassias, Möbius transformation and Einstein velocity addition meet in the hyperbolic geometry of Bolyai and Lobachevsky. It turns out that Möbius addition that is extracted from Möbius transformation of the complex disc and Einstein addition from his special theory of relativity are isomorphic in the sense of gyrovector spaces.

Citations

• Einstein's Special Relativity: The Hyperbolic Geometric Viewpoint

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