Bulletin of the
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Bull. Korean Math. Soc. 2022; 59(4): 1011-1018

Published online July 31, 2022 https://doi.org/10.4134/BKMS.b210603

Copyright © The Korean Mathematical Society.

Magnetic geodesics on the space of K\"{a}hler potentials

Sibel \c{S}ahin

Mimar Sinan Fine Arts University

Abstract

In this work, magnetic geodesics over the space of K\"{a}hler 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\`{e}re equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric K\"{a}hler potentials over toric K\"{a}hler manifolds.

Keywords: Magnetic geodesics, K\"{a}hler potentianls

MSC numbers: Primary 31C12, 32W20

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