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- Title
Ricci-flat metrics on the complexification of a compact rank one symmetric space.
- Authors
Stenzel, Matthew
- 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), where u 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 function f. To prove that the resulting metric is complete requires some techniques from symplectic geometry.
- Publication
Manuscripta Mathematica, 1993, Vol 80, Issue 1, p151
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/BF03026543