Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
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.
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2011-09-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2011.090 |
| _version_ | 1818584956096479232 |
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| author | Benjamin McKay |
| author_facet | Benjamin McKay |
| author_sort | Benjamin McKay |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-16T08:29:24Z |
| format | Article |
| id | doaj.art-c197e9a313d8496fb99cd68b8f9b25a4 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-16T08:29:24Z |
| publishDate | 2011-09-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-c197e9a313d8496fb99cd68b8f9b25a42022-12-21T22:37:54ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592011-09-017090Holomorphic Parabolic Geometries and Calabi-Yau ManifoldsBenjamin McKayWe 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.http://dx.doi.org/10.3842/SIGMA.2011.090parabolic geometryCalabi-Yau manifold |
| spellingShingle | Benjamin McKay Holomorphic Parabolic Geometries and Calabi-Yau Manifolds Symmetry, Integrability and Geometry: Methods and Applications parabolic geometry Calabi-Yau manifold |
| title | Holomorphic Parabolic Geometries and Calabi-Yau Manifolds |
| title_full | Holomorphic Parabolic Geometries and Calabi-Yau Manifolds |
| title_fullStr | Holomorphic Parabolic Geometries and Calabi-Yau Manifolds |
| title_full_unstemmed | Holomorphic Parabolic Geometries and Calabi-Yau Manifolds |
| title_short | Holomorphic Parabolic Geometries and Calabi-Yau Manifolds |
| title_sort | holomorphic parabolic geometries and calabi yau manifolds |
| topic | parabolic geometry Calabi-Yau manifold |
| url | http://dx.doi.org/10.3842/SIGMA.2011.090 |
| work_keys_str_mv | AT benjaminmckay holomorphicparabolicgeometriesandcalabiyaumanifolds |