Magnetic Geodesics on the Space of K\"ahler Potentials
Sibel Sahin
TL;DR
This paper investigates magnetic geodesics on the space of K"ahler potentials using variational methods, deriving equations and exploring their relation to complex Monge-Amp eplaced{é}{e}re equations, with special focus on toric K"ahler manifolds.
Contribution
It introduces a variational approach to magnetic geodesics on K"ahler potentials and connects these to perturbed complex Monge-Amp eplaced{é}{e}re equations, including special cases on toric manifolds.
Findings
Derived the magnetic geodesic equation in this setting
Linked magnetic geodesics to a perturbed complex Monge-Amp eplaced{é}{e}re equation
Analyzed the case of toric K"ahler potentials
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.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Waves and Solitons