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).