Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2021; 58(6): 1501-1511

Online first article August 31, 2021      Printed November 1, 2021

https://doi.org/10.4134/JKMS.j210147

Copyright © The Korean Mathematical Society.

Magnetic curves in $\mathbb{H}^3\times\mathbb{R}$

Zlatko Erjavec, Jun-ichi Inoguchi

Pavlinska 2, HR-42000, Vara{\v z}din; 1-1-1 Tennodai, Tsukuba 305-8571

Abstract

In this paper we study magnetic trajectories on $\mathbb{H}^3\times\mathbb{R}$ with respect to the strictly almost K{\"a}hler structure. We find three types of magnetic curves which correspond to the almost complex structure compatible to the product metric on $\mathbb{H}^3\times\mathbb{R}.$

Keywords: Magnetic curve, $\mathbb{H}^3\times\mathbb{R}$, almost K{\"a}hler structure

MSC numbers: Primary 53C15, 53C30, 53C55, 53C80

Supported by: The second named author is partially supported by JSPS KAKENHI Grant Number 19K03461.

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