Foundations of higher-order variational theory on Grassmann fibrations (Q2925092)
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scientific article; zbMATH DE number 6359102
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Foundations of higher-order variational theory on Grassmann fibrations |
scientific article; zbMATH DE number 6359102 |
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Foundations of higher-order variational theory on Grassmann fibrations (English)
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20 October 2014
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Grassmann fibration
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submanifold
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jet
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contact element
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homogeneity
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Lagran-Gian
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Lepage form
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invariance
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Noether current
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This paper is concerned with the higher-order global variational analysis on Grassmann fibrations. The authors study related integral variational principles for one-dimensional immersed submanifolds. This analysis is carried out by using differential 1-forms with specific properties. The main result deals with the study of prolongations of immersions and vector fields to the Grassmann fibrations, which are viewed as a geometric tool for the variations of immersions. The abstract results are illustrated with the derivation of the Euler-Lagrange equations for submanifolds and the Noether theorem on invariant variational functionals. Several related examples are provided in the final part of this paper.
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