Citation:McKay, B. (2017) 'Holomorphic geometric structures on Kähler–Einstein manifolds', manuscripta mathematica, 153(1), pp. 1-34. doi:10.1007/s00229-016-0873-8
We prove that the compact Kähler manifolds with c1≥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 c1≥0 that admit holomorphic cominiscule geometries are the locally Hermitian symmetric varieties.
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