Holomorphic Parabolic Geometries and Calabi-Yau Manifolds

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• ISSN: 1815-0659
• Main Author: McKay, B.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147392
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Holomorphic Parabolic Geometries and Calabi-Yau Manifolds / B. McKay // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 34 назв. — англ.

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.