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Twistor Geometry of Null Foliations in Complex Euclidean Space
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Twistor Geometry of Null Foliations in Complex Euclidean Space
Інший ID:
2010 Mathematics Subject Classification: 32L25; 53C28; 53C12
DOI:10.3842/SIGMA.2017.005
DOI:10.3842/SIGMA.2017.005
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
625
Завантажень:
244
Анотація:
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.
