An affine sphere equation associated to Einstein toric surfaces
Differential Geometry
2007-10-02 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.0710.0218,
title = {An affine sphere equation associated to Einstein toric surfaces},
author = {Toshiki Mabuchi},
journal= {arXiv preprint arXiv:0710.0218},
year = {2007}
}
Comments
to appear in the Proceedings of ICCM 2007, published by Higher Educational Press