A Gyrogeometric Mean in the Einstein Gyrogroup

A Gyrogeometric Mean in the Einstein Gyrogroup

In this paper, we define a gyrogeometric mean on the Einstein gyrovector space. It satisfies several properties one would expect for means. For example, it is permutation-invariant and left-translation invariant. It is already known that the Einstein gyrogroup is a gyrocommutative gyrogroup. We give...

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Veröffentlicht in:Symmetry (Basel) 2020-08, Vol.12 (8), p.1333
Hauptverfasser: Honma, Takuro, Hatori, Osamu
Format: Artikel
Sprache:eng
Schlagworte:
Einstein velocity addition
gyrogeometric mean
gyrogroup
Inequality
Invariants
Permutations
Theory of relativity
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Zusammenfassung:In this paper, we define a gyrogeometric mean on the Einstein gyrovector space. It satisfies several properties one would expect for means. For example, it is permutation-invariant and left-translation invariant. It is already known that the Einstein gyrogroup is a gyrocommutative gyrogroup. We give an alternative proof which depends only on an elementary calculation.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym12081333