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  • 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)
  • 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) (en)
Title
  • Foundations of higher-order variational theory on Grassmann fibrations
  • Foundations of higher-order variational theory on Grassmann fibrations (en)
skos:prefLabel
  • Foundations of higher-order variational theory on Grassmann fibrations
  • Foundations of higher-order variational theory on Grassmann fibrations (en)
skos:notation
  • RIV/62690094:18470/14:50002496!RIV15-MSM-18470___
http://linked.open...avai/riv/aktivita
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  • 17364
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  • RIV/62690094:18470/14:50002496
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  • Noether current.; invariance; Lepage form; Lagrangian; homogeneity; contact element; jet; submanifold; Grassmann fibration (en)
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  • US - Spojené státy americké
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  • [E372830A8F40]
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  • International journal of geometric methods in modern physics
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  • 11
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  • Krupka, Demeter
  • Urban, Zbyněk
http://linked.open...ain/vavai/riv/wos
  • 000341012300010
issn
  • 0219-8878
number of pages
http://bibframe.org/vocab/doi
  • 10.1142/S0219887814600238
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  • 18470
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