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

2009/12/02 by Abreu, Miguel
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0912.0491

Abstract

In these notes, after an introduction to toric Kahler geometry, we present Calabi's family of U(n)-invariant extremal Kahler metrics in symplectic action-angle coordinates and show that it actually contains, as particular cases, many interesting cohomogeneity one examples of constant scalar curvature.

Related

• Kahler geometry of toric varieties and extremal metrics
• Constant scalar curvature metrics on toric surfaces
• KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS
• The Kähler geometry of toric manifolds
• Metrics of Special Curvature with Symmetry