Nihonkai Mathematical Journal

A confirmation by hand calculation that the Möbius ball is a gyrovector space

Keiichi Watanabe

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We give a confirmation that the Möbius ball of any real inner product space is a gyrovector space by using only elementary hand calculation. Some remarks to [2] will also be made.


This work is partly supported by Grant-in-Aid for Scientific Research (C) Number 23540190, Japan Society for the Promotion of Science.

Article information

Nihonkai Math. J., Volume 27, Number 1-2 (2016), 99-115.

Received: 12 January 2016
Revised: 4 April 2016
First available in Project Euclid: 14 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51M10: Hyperbolic and elliptic geometries (general) and generalizations
Secondary: 20N05: Loops, quasigroups [See also 05Bxx] 46C99: None of the above, but in this section 51P05: Geometry and physics (should also be assigned at least one other classification number from Sections 70-86)

Möbius gyrogroups Möbius gyrovector spaces


Watanabe, Keiichi. A confirmation by hand calculation that the Möbius ball is a gyrovector space. Nihonkai Math. J. 27 (2016), no. 1-2, 99--115.

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