An affine sphere equation associated to Einstein toric surfaces

Abstract

As seen in the works of Calabi, Cheng-Yau and Loftin, affine sphere equations have a close relationship with Kaehler-Einstein metrics. The main purpose of this note is to show that an equation analogous to those of hyperbolic affine spheres arises naturally from Kaehler-Einstein metrics on Einstein toric surfaces. The case for the remaining toric surfaces with Kaehler-Ricci solitons will also be discussed.

to appear in the Proceedings of ICCM 2007, published by Higher Educational Press

References in corpus (2)

• Numerical Kaehler-Einstein metric on the third del Pezzo
• Numerical Kaehler-Ricci soliton on the second del Pezzo