Closed magnetic geodesics on closed hyperbolic Riemann surfaces
type: Item
instance of: scholarly article
title: Closed magnetic geodesics on closed hyperbolic Riemann surfaces
zbMATH Open document ID: 1252.53049
author: Matthias Schneider
publication date: 2012-08-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1009.1723
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 58E10
zbMATH DE Number: 6073827
zbMATH Keywords: magnetic geodesics
zbMATH Keywords: periodic geodesics
zbMATH Keywords: closed geodesics
zbMATH Keywords: Riemann surfaces
MaRDI profile type: Publication
OpenAlex ID: W3102405521
arXiv ID: 1009.1723
DOI: 10.1112/PLMS/PDS013
published in: Proceedings of the London Mathematical Society. Third Series
review text: A magnetic geodesic is a curve on a Riemannian manifold moving according to the usual geodesic equations modified by including a magnetic force term. The author proves the existence of Alexandrov embedded (a fortiori closed and null homotopic) magnetic geodesics with any sufficiently small kinetic energy, on any closed surface with sufficiently large negative curvature and sufficiently large positive magnetic force. The method uses an \(S^1\)-equivariant index formula for a certain vector field on an infinite dimensional Sobolev space of loops, and a compactness theorem for the space of Alexandrov embedded magnetic geodesic loops.
reviewed by: Benjamin McKay
description: scientific article; zbMATH DE number 6073827