An affine sphere equation associated to Einstein toric surfaces

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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

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Differential Geometry, Complex Variables, 32Q20; 53A15; 14M25

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http://salesiana.dossiersoluciones.com/handle/123456789/139062

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.0218
 http://arxiv.org/abs/0710.0218

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arXiv