Twistor Geometry of Null Foliations in Complex Euclidean Space

J 2017

Twistor Geometry of Null Foliations in Complex Euclidean Space

TAGHAVI-CHABERT, Arman

Basic information

Original name

Twistor Geometry of Null Foliations in Complex Euclidean Space

Authors

TAGHAVI-CHABERT, Arman (250 France, guarantor, belonging to the institution)

Edition

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, KYIV, NATL ACAD SCI UKRAINE, INST MATH, 2017, 1815-0659

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Ukraine

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 1.100

RIV identification code

RIV/00216224:14310/17:00094689

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.3842/SIGMA.2017.005

UT WoS

000393827700001

Keywords in English

twistor geometry; complex variables; foliations; spinors

Abstract

V originále

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.

Links

GP14-27885P, research and development project

Name: Skoro izotropní struktury v pseudo-riemannovské geometrii

Investor: Czech Science Foundation

Citovat

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.

@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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