2022 COMPLEX SCALAR MULTIPLICATIONS ON THE POINCARÉ DISK
Toshikazu Abe
Author Affiliations +
Nihonkai Math. J. 33(2): 39-43 (2022).

Abstract

The Poincaré disk is a typical example of a (real inner product) gyrovector spaces. In this paper, we show that the Poincaré disk cannot have a complex scalar multiplication in a natural sense.

Funding Statement

This work was supported by JSPS KAKENHI Grant Numbers JP22K03332.

Acknowledgements

The author is grateful to the referee for his/her valuable comments and suggestions.

Citation

Download Citation

Toshikazu Abe. "COMPLEX SCALAR MULTIPLICATIONS ON THE POINCARÉ DISK." Nihonkai Math. J. 33 (2) 39 - 43, 2022.

Information

Received: 15 November 2022; Revised: 30 November 2022; Published: 2022
First available in Project Euclid: 11 July 2023

MathSciNet: MR4622660
zbMATH: 1520.30055

Subjects:
Primary: 51M09

Keywords: Möbius gyrogroup , Poincaré disk

Rights: Copyright © 2022 Niigata University, Department of Mathematics

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Vol.33 • No. 2 • 2022
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