Calabi Energies of Extremal Toric Surfaces
Differential Geometry
2013-10-14 v2
Abstract
We derive a formula for the L^2 norm of the scalar curvature of any extremal Kaehler metric on a compact toric manifold, stated purely in terms of the geometry of the corresponding moment polytope. The main interest of this formula pertains to the case of complex dimension 2, where it plays a key role in construction of Bach-flat metrics on appropriate 4-manifolds.
Keywords
Cite
@article{arxiv.1110.0682,
title = {Calabi Energies of Extremal Toric Surfaces},
author = {Claude LeBrun},
journal= {arXiv preprint arXiv:1110.0682},
year = {2013}
}
Comments
28 pages. Published version. Added section on Abreu formalism generalizes main result to higher dimensions