Magnetic Geodesics on the Space of K\"ahler Potentials
Complex Variables
2020-07-09 v1 Differential Geometry
Abstract
In this work, magnetic geodesics over the space of K\"ahler potentials are studied through a variational method for a generalized Landau-Hall functional. The magnetic geodesic equation is calculated in this setting and its relation to a perturbed complex Monge-Amp\`ere equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric K\"ahler potentials over toric K\"ahler manifolds.
Keywords
Cite
@article{arxiv.2007.03918,
title = {Magnetic Geodesics on the Space of K\"ahler Potentials},
author = {Sibel Sahin},
journal= {arXiv preprint arXiv:2007.03918},
year = {2020}
}
Comments
8 pages