Pure spinors, intrinsic torsion and curvature in even dimensions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F16%3A00088801" target="_blank" >RIV/00216224:14310/16:00088801 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.difgeo.2016.02.006" target="_blank" >http://dx.doi.org/10.1016/j.difgeo.2016.02.006</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.difgeo.2016.02.006" target="_blank" >10.1016/j.difgeo.2016.02.006</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Pure spinors, intrinsic torsion and curvature in even dimensions

Popis výsledku v původním jazyce

We study the geometric properties of a $2m$-dimensional complex manifold $M$ admitting a holomorphic reduction of the frame bundle to the structure group $P subset Spin(2m, C)$, the stabiliser of the line spanned by a pure spinor at a point. Geometrically, $M$ is endowed with a holomorphic metric $g$, a holomorphic volume form, a spin structure compatible with $g$, and a holomorphic pure spinor field $xi$ up to scale. The defining property of $xi$ is that it determines an almost null structure, i.e. an $m$-plane distribution $N_xi$ along which $g$ is totally degenerate. We develop a spinor calculus, by means of which we encode the geometric properties of $N_xi$ corresponding to the algebraic properties of the intrinsic torsion of the $P$-structure. This is the failure of the Levi-Civita connection $nabla$ of $g$ to be compatible with the $P$ -structure. In a similar way, we examine the algebraic properties of the curvature of $nabla$. Applications to spinorial differential equations are given.

Název v anglickém jazyce

Pure spinors, intrinsic torsion and curvature in even dimensions

Popis výsledku anglicky

We study the geometric properties of a $2m$-dimensional complex manifold $M$ admitting a holomorphic reduction of the frame bundle to the structure group $P subset Spin(2m, C)$, the stabiliser of the line spanned by a pure spinor at a point. Geometrically, $M$ is endowed with a holomorphic metric $g$, a holomorphic volume form, a spin structure compatible with $g$, and a holomorphic pure spinor field $xi$ up to scale. The defining property of $xi$ is that it determines an almost null structure, i.e. an $m$-plane distribution $N_xi$ along which $g$ is totally degenerate. We develop a spinor calculus, by means of which we encode the geometric properties of $N_xi$ corresponding to the algebraic properties of the intrinsic torsion of the $P$-structure. This is the failure of the Levi-Civita connection $nabla$ of $g$ to be compatible with the $P$ -structure. In a similar way, we examine the algebraic properties of the curvature of $nabla$. Applications to spinorial differential equations are given.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GP14-27885P" target="_blank" >GP14-27885P: Skoro izotropní struktury v pseudo-riemannovské geometrii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Differential Geometry and its Applications

ISSN

0926-2245

e-ISSN

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Svazek periodika

46

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

40

Strana od-do

164-203

Kód UT WoS článku

000374599400010

EID výsledku v databázi Scopus

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