Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 090, 11 pages      arXiv:0812.1749      https://doi.org/10.3842/SIGMA.2011.090

Holomorphic Parabolic Geometries and Calabi-Yau Manifolds

Benjamin McKay
School of Mathematical Sciences, University College Cork, Cork, Ireland

Received May 25, 2011, in final form September 15, 2011; Published online September 20, 2011

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 Kähler manifolds.

Key words: parabolic geometry; Calabi-Yau manifold.

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