Calabi Energies of Extremal Toric Surfaces
Abstract
We derive a formula for the L2 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.
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