Some new domains with complete Kähler metrics of negative curvature

Abstract

We add to the known examples of complete Kahler manifolds with negative sectional curvature by showing that the following three classes of domains in euclidean spaces also belong: perturbations of ellipsoidal domains in ℂn, intersections of complex-ellipsoidal domains in ℂ2, and intersections of fractional linear transforms of the unit ball in ℂ2. In the process, we prove the following theorem in differential geometry: in the intersection of two complex-ellipsoidal domains in ℂ2, the sum of the Bergman metrics is a Kahler metric with negative curvature operator.