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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