Strominger–Yau–Zaslow geometry, Affine Spheres and Painlevé III
نویسنده
چکیده
We give a gauge invariant characterisation of the elliptic affine sphere equation and the closely related Tzitzéica equation as reductions of real forms of SL(3,C) anti–self–dual Yang–Mills equations by two translations, or equivalently as a special case of the Hitchin equation. We use the Loftin–Yau–Zaslow construction to give an explicit expression for a six–real dimensional semi–flat Calabi–Yau metric in terms of a solution to the affine-sphere equation and show how a subclass of such metrics arises from 3rd Painlevé transcendents. email [email protected] email [email protected]
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