Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F15%3A50004214" target="_blank" >RIV/62690094:18470/15:50004214 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/article/10.1007%2Fs10587-015-0230-1" target="_blank" >http://link.springer.com/article/10.1007%2Fs10587-015-0230-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10587-015-0230-1" target="_blank" >10.1007/s10587-015-0230-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Popis výsledku v původním jazyce

Let (M, g) be a 4-dimensional Einstein Riemannian manifold. At each point p of M , the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p. In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O(4) acts as a transformation group between ST bases at T p M and for the so-called 2-stein curvature tensors, the group Sp(1) acts as a transformation group between ST bases. In the present work, the complete list of Lie subgroups of SO(4) which act as transformation groups between ST bases for certain classes of Einstein curvature tensors is presented. Special representations of groups SO(2), T 2, Sp(1) or U(2) are obtained and the classes of curvature tensors whose transformation group into new ST bases is one of the mentioned groups are determined.

Název v anglickém jazyce

Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Popis výsledku anglicky

Let (M, g) be a 4-dimensional Einstein Riemannian manifold. At each point p of M , the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p. In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O(4) acts as a transformation group between ST bases at T p M and for the so-called 2-stein curvature tensors, the group Sp(1) acts as a transformation group between ST bases. In the present work, the complete list of Lie subgroups of SO(4) which act as transformation groups between ST bases for certain classes of Einstein curvature tensors is presented. Special representations of groups SO(2), T 2, Sp(1) or U(2) are obtained and the classes of curvature tensors whose transformation group into new ST bases is one of the mentioned groups are determined.

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

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Czechoslovak mathematical journal

ISSN

0011-4642

e-ISSN

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Svazek periodika

65

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

15

Strana od-do

1101-1115

Kód UT WoS článku

000367853700018

EID výsledku v databázi Scopus

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