Twistor Geometry of Null Foliations in Complex Euclidean Space
We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface Qⁿ of dimension n≥3, and its twistor space PT, defined to be the space of all linear subspaces of maximal dimension of Qⁿ. Viewing complex Euclidean space CEⁿ as a dense open subset of...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148560 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Twistor Geometry of Null Foliations in Complex Euclidean Space / A. Taghavi-Chabert // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862533008165175296 |
|---|---|
| author | Taghavi-Chabert, A. |
| author_facet | Taghavi-Chabert, A. |
| citation_txt | Twistor Geometry of Null Foliations in Complex Euclidean Space / A. Taghavi-Chabert // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface Qⁿ of dimension n≥3, and its twistor space PT, defined to be the space of all linear subspaces of maximal dimension of Qⁿ. Viewing complex Euclidean space CEⁿ as a dense open subset of Qⁿ, we show how local foliations tangent to certain integrable holomorphic totally null distributions of maximal rank on CEⁿ can be constructed in terms of complex submanifolds of PT. The construction is illustrated by means of two examples, one involving conformal Killing spinors, the other, conformal Killing-Yano 2-forms. We focus on the odd-dimensional case, and we treat the even-dimensional case only tangentially for comparison.
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| first_indexed | 2025-11-24T04:39:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148560 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:39:55Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Taghavi-Chabert, A. 2019-02-18T15:47:04Z 2019-02-18T15:47:04Z 2017 Twistor Geometry of Null Foliations in Complex Euclidean Space / A. Taghavi-Chabert // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 37 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 32L25; 53C28; 53C12 DOI:10.3842/SIGMA.2017.005 https://nasplib.isofts.kiev.ua/handle/123456789/148560 We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface Qⁿ of dimension n≥3, and its twistor space PT, defined to be the space of all linear subspaces of maximal dimension of Qⁿ. Viewing complex Euclidean space CEⁿ as a dense open subset of Qⁿ, we show how local foliations tangent to certain integrable holomorphic totally null distributions of maximal rank on CEⁿ can be constructed in terms of complex submanifolds of PT. The construction is illustrated by means of two examples, one involving conformal Killing spinors, the other, conformal Killing-Yano 2-forms. We focus on the odd-dimensional case, and we treat the even-dimensional case only tangentially for comparison. The author would like to thank Boris Doubrov, Lionel Mason and Jan Slov´ak for helpful discussions
 and comments, and the anonymous referees for their reports. He is also grateful to Lukas
 Vokrınek and Andreas Cap for clarifying some aspects of Section 2.5. This work was funded by
 a GACR (Czech Science Foundation) post-doctoral grant GP14-27885P. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Twistor Geometry of Null Foliations in Complex Euclidean Space Article published earlier |
| spellingShingle | Twistor Geometry of Null Foliations in Complex Euclidean Space Taghavi-Chabert, A. |
| title | Twistor Geometry of Null Foliations in Complex Euclidean Space |
| title_full | Twistor Geometry of Null Foliations in Complex Euclidean Space |
| title_fullStr | Twistor Geometry of Null Foliations in Complex Euclidean Space |
| title_full_unstemmed | Twistor Geometry of Null Foliations in Complex Euclidean Space |
| title_short | Twistor Geometry of Null Foliations in Complex Euclidean Space |
| title_sort | twistor geometry of null foliations in complex euclidean space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148560 |
| work_keys_str_mv | AT taghavichaberta twistorgeometryofnullfoliationsincomplexeuclideanspace |