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Holomorphic Parabolic Geometries and Calabi-Yau Manifolds

Keywords: parabolic geometry , Calabi-Yau manifold

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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 hler manifolds.

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