Abstract
We construct a complete Ricci-flat Kähler metric on the complexification of a compact rank one symmetric space. Our method is to look for a Kähler potential of the form ψ = ƒ(u), whereu satisfies the homogeneous Monge-Ampère equation. We use the high degree of symmetry present to reduce the non-linear partial differential equation governing the Ricci curvature to a simple second-order ordinary differential equation for the functionf. To prove that the resulting metric is complete requires some techniques from symplectic geometry.
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Stenzel, M.B. Ricci-flat metrics on the complexification of a compact rank one symmetric space. Manuscripta Math 80, 151–163 (1993). https://doi.org/10.1007/BF03026543
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DOI: https://doi.org/10.1007/BF03026543