On Hamilton–Poincaré field equations

Volume 110 / 2016

Santiago Capriotti, Juan Carlos Marrero Banach Center Publications 110 (2016), 9-24 MSC: Primary 70S05, 70S10; Secondary 53C42. DOI: 10.4064/bc110-0-1


We introduce the prolongation, to the reduced extended multimomentum bundle, of a vertical vector field (in the total space of the corresponding configuration bundle) which is invariant under the action of the symmetry Lie group. Using this construction, we present a geometric description of the Hamilton–Poincaré field equations associated with a symmetric Hamiltonian field theory. Finally, we discuss an example: the theory of minimal submanifolds of a Riemannian manifold.


  • Santiago CapriottiDepartamento de Matemática
    Universidad Nacional del Sur
    8000 Bahía Blanca, Argentina
  • Juan Carlos MarreroULL-CSIC Geometría Diferencial y Mecánica Geométrica
    Departamento de Matemáticas, Estadística e IO
    Sección de Matemáticas, Facultad de Ciencias
    Universidad de La Laguna
    La Laguna, Tenerife, Canary Islands, Spain

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