2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139062As 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 PressDifferential GeometryComplex Variables32Q20; 53A15; 14M25text