ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53, 83 Zuev, Sergey V., Penza State Pedagogical University, Russia Analytic continuations of SU(2n)-invariant Ricci-flat Kähler metric Kähler manifold is 2n-dimensional Riemannian manifold equipped with integrable complex structure. The manifold is called Ricci-flat if it has vanished Ricci tensor. In case of dimension four Kähler Ricci-flat manifold admits three covariantly constant complex structure and it is hyperKähler manifold. Present author constructed a family of Kähler Ricci-flat metrics for an arbitrary dimension 4n supposed that they are invariant under SU(2n)-transformations. But these metrics are incomplete. Some analitic continuations will be presented. Reference: Zuev S. V. A 4n-dimensional Kähler Ricci-flat metric. Proc. Int. Conf. “Geometrization of Physics III”, Kazan State University. – October 1-5, 1997, Kazan, Russia. – To appear.