Foundations of higher-order variational theory on Grassmann fibrations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F14%3A50002496" target="_blank" >RIV/62690094:18470/14:50002496 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S0219887814600238" target="_blank" >http://dx.doi.org/10.1142/S0219887814600238</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219887814600238" target="_blank" >10.1142/S0219887814600238</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Foundations of higher-order variational theory on Grassmann fibrations

Popis výsledku v původním jazyce

A setting for higher-order global variational analysis on Grassmann fibrations is presented. The integral variational principles for one-dimensional immersed submanifolds are introduced by means of differential 1-forms with specific properties, similar to the Lepage forms from the variational calculus on fibred manifolds. Prolongations of immersions and vector fields to the Grassmann fibrations are defined as a geometric tool for the variations of immersions, and the first variation formula in the infinitesimal form is derived. Its consequences, the Euler-Lagrange equations for submanifolds and the Noether theorem on invariant variational functionals are proved. Examples clarifying the meaning of the Noether theorem in the context of variational principles for submanifolds are given. (pp.1460023-1 - 1460023-27)

Název v anglickém jazyce

Foundations of higher-order variational theory on Grassmann fibrations

Popis výsledku anglicky

A setting for higher-order global variational analysis on Grassmann fibrations is presented. The integral variational principles for one-dimensional immersed submanifolds are introduced by means of differential 1-forms with specific properties, similar to the Lepage forms from the variational calculus on fibred manifolds. Prolongations of immersions and vector fields to the Grassmann fibrations are defined as a geometric tool for the variations of immersions, and the first variation formula in the infinitesimal form is derived. Its consequences, the Euler-Lagrange equations for submanifolds and the Noether theorem on invariant variational functionals are proved. Examples clarifying the meaning of the Noether theorem in the context of variational principles for submanifolds are given. (pp.1460023-1 - 1460023-27)

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

International journal of geometric methods in modern physics

ISSN

0219-8878

e-ISSN

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Svazek periodika

11

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

1-27

Kód UT WoS článku

000341012300010

EID výsledku v databázi Scopus

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