Tohoku Mathematical Journal
2017
March
SECOND SERIES VOL. 69, NO. 1

Tohoku Math. J.
69 (2017), 113-128

Title PERIODIC MAGNETIC CURVES IN BERGER SPHERES

Author Jun-ichi Inoguchi and Marian Ioan Munteanu

(Received January 5, 2015, revised May 25, 2015)
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 ${\mathbb{S}}^3$.

Mathematics Subject Classification. Primary 53C15; Secondary 53C25, 53C30, 37J45, 53C80.
Key words and phrases. Magnetic field, Berger sphere, elliptic Sasakian space form, Hopf torus, periodic curve.

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