Tensor Decompositions and Their Properties

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F23%3A73619705" target="_blank" >RIV/61989592:15310/23:73619705 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/11/17/3638" target="_blank" >https://www.mdpi.com/2227-7390/11/17/3638</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math11173638" target="_blank" >10.3390/math11173638</a>

Result language
angličtina
Original language name
Tensor Decompositions and Their Properties
Original language description
In the present paper, we study two different approaches of tensor decomposition. The first part aims to study some properties of tensors that result from the fact that some components are vanishing in certain coordinates. It is proven that these conditions allow tensor decomposition, especially (1, s), s = 1, 2, 3 tensors. We apply the results for special tensors such as the Riemann, Ricci, Einstein, and Weyl tensors and the deformation tensors of affine connections. Thereby, we find new criteria for the Einstein spaces, spaces of constant curvature, and projective and conformal flat spaces. Further, the proof of the theorem of Mikeš and Moldobayev is repaired. It has been used in many works and it is a generalization of the criteria formulated by Schouten and Struik. The second part deals with the properties of a special differential operator with respect to the general decomposition of tensor fields on manifolds with affine connection. It is shown that the properties of special differential operators are transferred to the components of a given decomposition.
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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