One component of the curvature tensor of a Lorentzian manifold

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F10%3A00043842" target="_blank" >RIV/00216224:14310/10:00043842 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
One component of the curvature tensor of a Lorentzian manifold
Original language description
The holonomy algebra $g$ of an $n+2$-dimensional Lorentzian manifold $(M,g)$ admitting a parallel distribution of isotropic lines is contained in the subalgebra $simil(n)=(Realoplusso(n))zrReal^nsubsetso(1,n+1)$. An important invariant of $g$ is its $so(n)$-projection $hsubsetso(n)$, which is a Riemannian holonomy algebra. One component of the curvature tensor of the manifold belongs to the space $P(h)$ consisting of linear maps from $Real^n$ to $h$ satisfying an identity similar to the Bianchi one. In the present paper the spaces $P(h)$ are computed for each possible $h$. This gives the complete description of the values of the curvature tensor of the manifold $(M,g)$. These results can be applied e.g. to the holonomy classification of the Einstein Lorentzian manifolds.
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/GP201%2F09%2FP039" target="_blank" >GP201/09/P039: Holonomy of Riemannian supermanifolds and related geometric structures</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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