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2017 Periodic magnetic curves in Berger spheres
Jun-ichi Inoguchi, Marian Ioan Munteanu
Tohoku Math. J. (2) 69(1): 113-128 (2017). DOI: 10.2748/tmj/1493172131

Abstract

It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe it. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criterion for periodicity of magnetic curves on the unit sphere ${\mathbb{S}}^3$.

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Jun-ichi Inoguchi. Marian Ioan Munteanu. "Periodic magnetic curves in Berger spheres." Tohoku Math. J. (2) 69 (1) 113 - 128, 2017. https://doi.org/10.2748/tmj/1493172131

Information

Published: 2017
First available in Project Euclid: 26 April 2017

zbMATH: 1367.53040
MathSciNet: MR3640017
Digital Object Identifier: 10.2748/tmj/1493172131

Subjects:
Primary: 53C15
Secondary: 37J45 , 53C25 , 53C30 , 53C80

Keywords: Berger sphere , elliptic Sasakian space form , Hopf torus , magnetic field , periodic curve

Rights: Copyright © 2017 Tohoku University

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Vol.69 • No. 1 • 2017
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