Holomorphic geometric structures on Kaehler-Einstein manifolds
Differential Geometry
2019-11-12 v3
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.
Cite
@article{arxiv.1308.1613,
title = {Holomorphic geometric structures on Kaehler-Einstein manifolds},
author = {Benjamin McKay},
journal= {arXiv preprint arXiv:1308.1613},
year = {2019}
}