| TAGHAVI-CHABERT, Arman. Twistor Geometry of Null Foliations in Complex Euclidean Space. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. KYIV: NATL ACAD SCI UKRAINE, INST MATH, 2017, vol. 13, No 1, p. nestrankovano, 42 pp. ISSN 1815-0659. Available from: https://dx.doi.org/10.3842/SIGMA.2017.005. |
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@article{1376696,
author = {TaghaviandChabert, Arman},
article_location = {KYIV},
article_number = {1},
doi = {http://dx.doi.org/10.3842/SIGMA.2017.005},
keywords = {twistor geometry; complex variables; foliations; spinors},
language = {eng},
issn = {1815-0659},
journal = {SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS},
title = {Twistor Geometry of Null Foliations in Complex Euclidean Space},
volume = {13},
year = {2017}
}
TY - JOUR
ID - 1376696
AU - Taghavi-Chabert, Arman
PY - 2017
TI - Twistor Geometry of Null Foliations in Complex Euclidean Space
JF - SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
VL - 13
IS - 1
SP - nestrankovano
EP - nestrankovano
PB - NATL ACAD SCI UKRAINE, INST MATH
SN - 18150659
KW - twistor geometry
KW - complex variables
KW - foliations
KW - spinors
N2 - We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface $\mathcal{Q}^n$ of dimension $n \geq 3$, and its twistor space $\mathbb{PT}$, defined to be the space of all linear subspaces of maximal dimension of $\mathcal{Q}^n$. Viewing complex Euclidean space $\mathbb{CE}^n$ as a dense open subset of $\mathval{Q}^n$ , we show how local foliations tangent to certain integrable holomorphic totally null distributions of maximal rank on $\mathbb{CE}^n$ can be constructed in terms of complex submanifolds of $\mathbb{PT}$. 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.
ER -
TAGHAVI-CHABERT, Arman. Twistor Geometry of Null Foliations in Complex Euclidean Space. \textit{SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS}. KYIV: NATL ACAD SCI UKRAINE, INST MATH, 2017, vol.~13, No~1, p.~nestrankovano, 42 pp. ISSN~1815-0659. Available from: https://dx.doi.org/10.3842/SIGMA.2017.005.
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