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Mathematics > Differential Geometry

arXiv:0710.0218 (math)
[Submitted on 1 Oct 2007]

Title:An affine sphere equation associated to Einstein toric surfaces

Authors:Toshiki Mabuchi
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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.
Comments: to appear in the Proceedings of ICCM 2007, published by Higher Educational Press
Subjects: Differential Geometry (math.DG); Complex Variables (math.CV)
MSC classes: 32Q20; 53A15; 14M25
Cite as: arXiv:0710.0218 [math.DG]
  (or arXiv:0710.0218v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.0218

Submission history

From: Toshiki Mabuchi [view email]
[v1] Mon, 1 Oct 2007 07:44:46 UTC (9 KB)
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