I. V. Mykytyuk, “Classification of Ricci-flat metrics on the cotangent bundles of compact rank-one symmetric spaces”, Mat. Sb., 2011, Volume 202, Number 2,Pages <nobr>107

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

I. V. Mykytyuk^ab

^a Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine
^b Institute of Mathematics, Pedagogical University of Cracow

Abstract: 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.

Keywords: Ricci-flat Kähler metrics, Stenzel manifolds.

UDC: 514.765.1+512.813.4

MSC: 32Q15, 37J15

Received: 01.09.2009 and 15.04.2010

DOI: 10.4213/sm7627