Tensor Decompositions and Their Properties

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Tensor Decompositions and Their Properties

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Tensor Decompositions and Their Properties

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Svazek periodika

11

Číslo periodika v rámci svazku

17

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

13

Strana od-do

"3638-1"-"3638-13"

Kód UT WoS článku

001061104900001

EID výsledku v databázi Scopus

2-s2.0-85176443233