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Mathematics  2008 

Holomorphic Parabolic Geometries and Calabi-Yau Manifolds

DOI: 10.3842/SIGMA.2011.090

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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 K\"ahler manifolds.

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