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, Volume 80, Issue 1, pp 151–163 | Cite as

Ricci-flat metrics on the complexification of a compact rank one symmetric space

  • Matthew B. Stenzel
Article

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.

Keywords

Symmetric Space Ricci Curvature Cotangent Bundle Stein Manifold Real Projective Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Matthew B. Stenzel
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaRiverside

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