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Integrability of second-order Lagrangians admitting a first-order Hamiltonian formalism

Authors
Journal
Differential Geometry and its Applications
0926-2245
Publisher
Elsevier
Volume
35
Identifiers
DOI: 10.1016/j.difgeo.2014.04.006
Keywords
  • Einstein'S Equations
  • Hamilton–Cartan Formalism
  • Jet Bundles
  • Lagrangian Density
  • Poincaré–Cartan Form

Abstract

Abstract Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) necessary and sufficient conditions for the Poincaré–Cartan form of a second-order Lagrangian on an arbitrary fibred manifold p:E→N to be projectable onto J1E are explicitly determined; ii) for each of such Lagrangians, a first-order Hamiltonian formalism is developed and a new notion of regularity is introduced; iii) the variational problems of this class defined by regular Lagrangians are proved to be involutive.

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