This article is cited in 3 papers

Holomorphic Parabolic Geometries and Calabi–Yau Manifolds

Benjamin McKay

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

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.

Keywords: parabolic geometry, Calabi–Yau manifold.

MSC: 53C55; 53A55; 53C10

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

Language: English

DOI: 10.3842/SIGMA.2011.090

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ArXiv: 0812.1749