Calabi Energies of Extremal Toric Surfaces

Details Calabi Energies of Extremal Toric Surfaces Calabi Energies of Extremal Toric Surfaces

2011-10-04

arxiv.org/abs/1110.0682v1

Mathematics

Differential Geometry

34 pages

Scientific paper

We derive a formula for the L^2 norm of the scalar curvature of any extremal
Kaehler metric on a compact complex toric surface, stated purely in terms of
the geometry of the corresponding moment polygon. We then describe some
applications of this formula to the construction of 4-manifolds with vanishing
Bach tensor.

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