Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 8

Magnetic curves in the real special linear group

Pages: 2161 – 2205

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n8.a6

Authors

Jun-Ichi Inoguchi (Institute of Mathematics, University of Tsukuba, Japan)

Marian Ioan Munteanu (Faculty of Mathematics, University ‘Al. I. Cuza’, Iasi, Romania)

Abstract

We investigate contact magnetic curves in the real special linear group of degree $2$. They are geodesics of the Hopf tubes over the projection curve. We prove that periodic contact magnetic curves in $\mathrm{SL}_2 \mathbb{R}$ can be quantized in the set of rational numbers. Finally, we study contact homogeneous magnetic trajectories in $\mathrm{SL}_2 \mathbb{R}$ and show that they project to horocycles in $\mathbb{H}^2 (-4)$.

This work was partially supported by Kakenhi 15K04834 and 19K03461 (Japan).

The second-named author is supported by the project funded by the Ministry of Research and Innovation within Program 1 – Development of the national RD system, Subprogram 1.2 – Institutional Performance – RDI excellence funding projects, Contract no. 34PFE/19.10.2018.