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

Abstract

We prove that if a Calabi--Yau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact Kähler manifolds. We also classify all holomorphic Cartan geometries on rationally connected complex projective manifolds.

7 pages

Cited by in corpus (2)

• Logarithmic Cartan geometry on complex manifolds
• Generalized Holomorphic Cartan geometries