Holomorphic Parabolic Geometries and Calabi-Yau Manifolds

Abstract

We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.

References in corpus (2)

• Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves
• Holomorphic Cartan geometries and Calabi--Yau manifolds

Cited by in corpus (4)

• Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves
• Extension Phenomena for Holomorphic Geometric Structures
• Holomorphic geometric structures on Kaehler-Einstein manifolds
• The Hartogs extension phenomenon for holomorphic parabolic and reductive geometries