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...
Saved in:
| Date: | 2017 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2017
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148560 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
|---|