A new infinite order formulation of variational sequences

Raffaele Vitolo

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 4, page 483-504
  • ISSN: 0044-8753

Abstract

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The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition and in the computations. We think that our infinite order approach could be easily applied in concrete situations, due to the conceptual simplicity of the scheme.

How to cite

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Vitolo, Raffaele. "A new infinite order formulation of variational sequences." Archivum Mathematicum 034.4 (1998): 483-504. <http://eudml.org/doc/248213>.

@article{Vitolo1998,
abstract = {The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition and in the computations. We think that our infinite order approach could be easily applied in concrete situations, due to the conceptual simplicity of the scheme.},
author = {Vitolo, Raffaele},
journal = {Archivum Mathematicum},
keywords = {fibred manifold; jet space; infinite order jet space; variational bicomplex; variational sequence 483504; fibred manifold; jet space; infinite order jet space; variational bicomplex; variational sequence},
language = {eng},
number = {4},
pages = {483-504},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A new infinite order formulation of variational sequences},
url = {http://eudml.org/doc/248213},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Vitolo, Raffaele
TI - A new infinite order formulation of variational sequences
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 4
SP - 483
EP - 504
AB - The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition and in the computations. We think that our infinite order approach could be easily applied in concrete situations, due to the conceptual simplicity of the scheme.
LA - eng
KW - fibred manifold; jet space; infinite order jet space; variational bicomplex; variational sequence 483504; fibred manifold; jet space; infinite order jet space; variational bicomplex; variational sequence
UR - http://eudml.org/doc/248213
ER -

References

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