Transformations between Singer-Thorpe bases in 4-dimensional Einstein manifolds
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10319187" target="_blank" >RIV/00216208:11320/15:10319187 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/15:50003621
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Transformations between Singer-Thorpe bases in 4-dimensional Einstein manifolds
Original language description
It is well known that, at each point of a 4-dimensional Einstein Riemannian manifold (M, g), the tangent space admits at least one so-called Singer-Thorpe basis with respect to the curvature tensor R at p. K. Sekigawa put the question "how many" Singer-Thorpe bases exist for a fixed curvature tensor R. Here we work only with algebraic structures (V, <,>, R), where <,> is a positive scalar product and R is an algebraic curvature tensor (in the sense of P. Gilkey) which satisfies the Einstein property. Wegive a partial answer to the Sekigawa problem and we state a reasonable conjecture for the general case. Moreover, we solve completely a modified problem: how many there are orthonormal bases which are Singer-Thorpe bases simultaneously for a natural 5-dimensional family of Einstein curvature tensors R. The answer is given by what we call "the universal Singer-Thorpe group" and we show that it is a finite group with 2304 elements.
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/GAP201%2F11%2F0356" target="_blank" >GAP201/11/0356: Riemannian, pseudo-Riemannian and affine differential geometry</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Hokkaido Mathematical Journal
ISSN
0385-4035
e-ISSN
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Volume of the periodical
44
Issue of the periodical within the volume
3
Country of publishing house
JP - JAPAN
Number of pages
18
Pages from-to
441-458
UT code for WoS article
000367966200009
EID of the result in the Scopus database
2-s2.0-84950264981