On different geometric formulations of Lagrangian formalism
type: Item
instance of: scholarly article
title: On different geometric formulations of Lagrangian formalism
zbMATH Open document ID: 0930.58001
DOI: 10.1016/S0926-2245(99)00011-X
author: Raffaele Vitolo
published in: Differential Geometry and its Applications
publication date: 1999-09-22T00:00:00Z
review text: We consider two geometric formulations of Lagrangian formalism on fibred manifolds: Krupka's theory of finite order variational sequences, and Vinogradov's infinite order variational sequence associated with the \(C\)-spectral sequence. On the one hand, we show that the direct limit of Krupka's variational bicomplex is a new infinite order variational bicomplex which yields a new infinite order variational sequence. On the other hand, by means of Vinogradov's \(C\)-spectral sequence, we provide a new finite order variational sequence whose direct limit turns out to be Vinogradov's infinite order variational sequence. Finally, we provide an equivalence of the two finite order and infinite order variational sequences up to the space of Euler-Lagrange morphisms.
Mathematics Subject Classification ID: 58A12
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 58J10
zbMATH DE Number: 1339066
zbMATH Keywords: fibred manifold
zbMATH Keywords: infinite order jet space
zbMATH Keywords: variational bicomplex
zbMATH Keywords: variational sequence
zbMATH Keywords: spectral sequence
MaRDI profile type: Publication
Wikidata QID: Q57555758
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description: scientific article; zbMATH DE number 1339066