English

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