Holomorphic geometric structures on Kaehler-Einstein manifolds

摘要

We prove that the compact Kaehler manifolds with first Chern classnonnegative that admit holomorphic parabolic geometries are the flat bundles ofrational homogeneous varieties over complex tori. We also prove that thecompact Kaehler manifolds with negative first Chern class that admitholomorphic cominiscule geometries are the locally Hermitian symmetricvarieties.