Construction of negatively curved complete intersections

Abstract

Using the Donaldson–Auroux theory, we construct complete intersections in complex projective manifolds, which are negatively curved in various ways. In particular, we prove the existence of compact simply connected Kähler manifolds with negative holomorphic bisectional curvature. We also construct hyperbolic hypersurfaces, and we obtain bounds for their Kobayashi hyperbolic metric.