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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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Інститут математики НАН України
2017
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148560 |
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irk-123456789-1485602019-02-19T01:25:41Z Twistor Geometry of Null Foliations in Complex Euclidean Space Taghavi-Chabert, A. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148560 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Taghavi-Chabert, A. |
| spellingShingle |
Taghavi-Chabert, A. Twistor Geometry of Null Foliations in Complex Euclidean Space Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Taghavi-Chabert, A. |
| author_sort |
Taghavi-Chabert, A. |
| title |
Twistor Geometry of Null Foliations in Complex Euclidean Space |
| title_short |
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_sort |
twistor geometry of null foliations in complex euclidean space |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148560 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT taghavichaberta twistorgeometryofnullfoliationsincomplexeuclideanspace |
| first_indexed |
2023-05-20T17:29:44Z |
| last_indexed |
2023-05-20T17:29:44Z |
| _version_ |
1796153422792097792 |