Pure spinors, intrinsic torsion and curvature in even dimensions

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Pure spinors, intrinsic torsion and curvature in even dimensions
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GP14-27885P" target="_blank" >GP14-27885P: Almost null structures in pseudo-riemannian geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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