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arXiv · 1110.0682

Calabi Energies of Extremal Toric Surfaces

Claude LeBrun
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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.

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Claude LeBrun. 2013-10-11. Calabi Energies of Extremal Toric Surfaces. https://arxiv.org/abs/1110.0682

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