Holomorphic geometric structures on Kaehler-Einstein manifolds

Abstract

We prove that the compact Kaehler manifolds with first Chern class nonnegative that admit holomorphic parabolic geometries are the flat bundles of rational homogeneous varieties over complex tori. We also prove that the compact Kaehler manifolds with negative first Chern class that admit holomorphic cominiscule geometries are the locally Hermitian symmetric varieties.

References in corpus (2)

• Locally homogeneous geometric manifolds
• Holomorphic Parabolic Geometries and Calabi-Yau Manifolds

Cited by in corpus (1)

• The Hartogs extension phenomenon for holomorphic parabolic and reductive geometries