Solvability of ODEs describing curves on $\mathbb{S}^2$ or $\mathbb{H}^2$
Commun. Korean Math. Soc. 2021 Vol. 36, No. 3, 549-555
https://doi.org/10.4134/CKMS.c200240
Published online May 12, 2021
Printed July 31, 2021
Hyungjin Huh
Chung-Ang University
Abstract : 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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