The variational sequence: Local and global properties

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F00%3A00000047" target="_blank" >RIV/47813059:19610/00:00000047 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

The variational sequence: Local and global properties

Popis výsledku v původním jazyce

The aim of this paper is to discuss some aspects of local and global properties of the Euler-Lagrange and Helmholtz-Sonin mappings of the calculus of variations in the r-th order field theory, i.e. on r-jet prolongations of fibered manifolds over a n-dimensional base with n>1, within the framework of the variational sequence, i.e. the quotient of the De Rham sequence with respect to its subsequence of contact differential forms. Such a discussion is, in general, based on the concept of sheaves of differential forms. In the paper a globally defined representation of the variational sequence by forms is constructed which is closely related to the standard concepts in the calculus of variations. There is a close relationship between elements of the quotient sheaves (classes of forms) and the quotient mappings on one hand and the standard objects of the calculus of variations, as lagrangians, Euler-Lagrange and Helmholtz-Sonin forms, and Euler-Lagrange and Helmholtz-Sonin mappings on the o

Název v anglickém jazyce

The variational sequence: Local and global properties

Popis výsledku anglicky

The aim of this paper is to discuss some aspects of local and global properties of the Euler-Lagrange and Helmholtz-Sonin mappings of the calculus of variations in the r-th order field theory, i.e. on r-jet prolongations of fibered manifolds over a n-dimensional base with n>1, within the framework of the variational sequence, i.e. the quotient of the De Rham sequence with respect to its subsequence of contact differential forms. Such a discussion is, in general, based on the concept of sheaves of differential forms. In the paper a globally defined representation of the variational sequence by forms is constructed which is closely related to the standard concepts in the calculus of variations. There is a close relationship between elements of the quotient sheaves (classes of forms) and the quotient mappings on one hand and the standard objects of the calculus of variations, as lagrangians, Euler-Lagrange and Helmholtz-Sonin forms, and Euler-Lagrange and Helmholtz-Sonin mappings on the o

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2000

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the Seminar on Differential Geometry

ISBN

ISBN80-7248-104

ISSN

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e-ISSN

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Počet stran výsledku

24

Strana od-do

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Název nakladatele

Slezská Univerzita v Opavě, Opava

Místo vydání

Opava, ČR

Místo konání akce

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Datum konání akce

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Typ akce podle státní příslušnosti

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Kód UT WoS článku

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