Covariant derivative of the curvature tensor of pseudo-Kahlerian manifolds

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F17%3A00100713" target="_blank" >RIV/00216224:14310/17:00100713 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/17:50005626
Result on the web
<a href="https://link.springer.com/article/10.1007/s10455-016-9533-1" target="_blank" >https://link.springer.com/article/10.1007/s10455-016-9533-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10455-016-9533-1" target="_blank" >10.1007/s10455-016-9533-1</a>

Result language
angličtina
Original language name
Covariant derivative of the curvature tensor of pseudo-Kahlerian manifolds
Original language description
It is well known that the curvature tensor of a pseudo-Riemannian manifold can be decomposed with respect to the pseudo-orthogonal group into the sum of the Weyl conformal curvature tensor, the traceless part of the Ricci tensor and of the scalar curvature. A similar decomposition with respect to the pseudo-unitary group exists on a pseudo-Kahlerian manifold; instead of the Weyl tensor one obtains the Bochner tensor. In the present paper, the known decomposition with respect to the pseudo-orthogonal group of the covariant derivative of the curvature tensor of a pseudo-Riemannian manifold is refined. A decomposition with respect to the pseudo-unitary group of the covariant derivative of the curvature tensor for pseudo-Kahlerian manifolds is obtained. This defines natural classes of spaces generalizing locally symmetric spaces and Einstein spaces. It is shown that the values of the covariant derivative of the curvature tensor for a non-locally symmetric pseudo-Riemannian manifold with an irreducible connected holonomy group different from the pseudo-orthogonal and pseudo-unitary groups belong to an irreducible module of the holonomy group.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA14-02476S" target="_blank" >GA14-02476S: Variations, geometry and physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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