## Nihonkai Mathematical Journal

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

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

#### Abstract

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.

#### Note

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

#### Article information

**Source**

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

**Dates**

Received: 12 January 2016

Revised: 4 April 2016

First available in Project Euclid: 14 September 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.nihmj/1505419744

**Mathematical Reviews number (MathSciNet)**

MR3698244

**Zentralblatt MATH identifier**

1382.51014

**Subjects**

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)

**Keywords**

Möbius gyrogroups Möbius gyrovector spaces

#### Citation

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. https://projecteuclid.org/euclid.nihmj/1505419744