Український математичний конгрес - 2009
Ihor Mykytyuk (Institute for Applied Problems of Mechanics and Mathematics, L'viv, Ukraine)
Classification of Ricci-flat complete Kahler metrics on the cotangent bundles of rank-one compact symmetric
All G-invariant Ricci-flat complete Kahler metrics on the cotangent bundles T*(G/K) of rank-one compact symmetric spaces G/K with the canonical symplectic form Ω as the Kahler form are classified (up to the action of the group of all symplectic diffeomorphisms). It is shown that classes of such metrics are parameterized by positive real numbers. Moreover, it is proved that the Ricci-flat complete Kahler metrics constructed by Stenzel are diffeomorphic to these one (with the canonical symplectic form Ω as the Kahler form).