Poincaré-Cartan Forms in Higher Order Variational Calculus on Fibred Manifolds.

• Autores: Jaime Muñoz Masqué
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 1, Nº 4, 1985, págs. 85-126
• Idioma: inglés
• Títulos paralelos:
  • Formas de Poincaré-Cartan en el cálculo variacional de orden superior sobre variedades fibradas
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• Resumen

  • The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted the interest of being able to work with a general formalism for higher order variational problems (see for instance [5], [7], [8]).