Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2021; 36(3): 549-555

Online first article May 12, 2021      Printed July 31, 2021

https://doi.org/10.4134/CKMS.c200240

Copyright © The Korean Mathematical Society.

Solvability of ODEs describing curves on $\mathbb{S}^2$ or $\mathbb{H}^2$

Hyungjin Huh

Chung-Ang University

Abstract

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We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

Keywords: Curves on sphere, curve on hyperbolic space, explicit solution formula

MSC numbers: 35B40, 35C05, 35Q41

Supported by: This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (2020R1F1A1A01072197).

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