Tulczyjew's triples and lagrangian submanifolds in classical field theories

2003/02/11 by Manuel de León, David Martı́n de Diego, de Leon, M. +6 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #math-ph #math.DG #math.MP #msc:53C15 #msc:53D12 #msc:70S05

paper · pdf · doi:10.48550/arxiv.math-ph/0302026

29 pages

arxiv created 2003/02/11 · arxiv updated 2016/09/07

Abstract

In this paper the notion of Tulczyjew's triples in classical mechanics is extended to classical field theories, using the so-called multisymplectic formalism, and a convenient notion of lagrangian submanifold in multisymplectic geometry. Accordingly, the dynamical equations are interpreted as the local equations defining these lagrangian submanifolds.

Cited by

• Skinner--Rusk formalism of action-dependent multicontact field theories
• Classical field theories of first order and Lagrangian submanifolds of premultisymplectic manifolds
• Geometric aspects of nonholonomic field theories

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