Classification of Ricci-flat metrics on the cotangent bundles of compact rank-one symmetric spaces

摘要

All complete Ricci-flat K?hler G-invariant metrics (g, J,) on the cotangent bundle of a compact rank-one symmetric space G/K, dimG/K > 3 (with the fixed K?hler form, the canonical symplectic structure), are classified. It is proved that the set of equivalence classes of such metrics can be parametrized by positive numbers. The representative of each class is constructed by using explicit expressions. An alternative description of these structures based on the K?hler reduction procedure is proposed. We show also that the complete Ricci-flat K?hler metrics, constructed by Stenzel, are diffeomorphic to these ones.