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

I. V. Mykytyuk

Sbornik. Mathematics, Tome 202 (2011) no. 2, pp. 257-278

Résumé

All complete Ricci-flat Kähler $G$-invariant metrics $(\mathbf g,J,\Omega)$ on the cotangent bundle of a compact rank-one symmetric space $G/K$, $\dim G/K\geqslant 3$ (with the fixed Kähler form, the canonical symplectic structure $\Omega$), 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 Kähler reduction procedure is proposed. We show also that the complete Ricci-flat Kähler metrics, constructed by Stenzel, are diffeomorphic to these ones. Bibliography: 26 titles.

Détail

Keywords: Stenzel manifolds.
Mots-clés : Ricci-flat Kähler metrics

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