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Holomorphic geometric structures on Kähler–Einstein manifolds

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Abstract

We prove that the compact Kähler manifolds with \(c_{1} \ge 0\) that admit holomorphic parabolic geometries are the flat bundles of rational homogeneous varieties over complex tori. We also prove that the compact Kähler manifolds with \(c_{1} \ge 0\) that admit holomorphic cominiscule geometries are the locally Hermitian symmetric varieties.

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  1. University College Cork, National University of Ireland, Cork, Ireland

    Benjamin McKay

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  1. Benjamin McKay
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Correspondence to Benjamin McKay.

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This publication has emanated from activity conducted with the financial support of Science Foundation Ireland under the International Strategic Cooperation Award Grant Number SFI/13/ISCA/2844.

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McKay, B. Holomorphic geometric structures on Kähler–Einstein manifolds. manuscripta math. 153, 1–34 (2017). https://doi.org/10.1007/s00229-016-0873-8

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