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In these notes, after an introduction to toric Kahler geometry, we presentCalabi's family of U(n)-invariant extremal Kahler metrics in symplecticaction-angle coordinates and show that it actually contains, as particularcases, many interesting cohomogeneity one examples of constant scalarcurvature.

Toric Kahler Metrics: Cohomogeneity One Examples of Constant Scalar Curvature in Action-Angle Coordinates