RT Journal Article T1 Constraints in Euler-Poincaré Reduction of FieldTheories A1 Castrillón López, Marco AB The goal of this short note is to show the geometric structure of the Euler-Poincaré reduction procedure in Field Theories with special emphasis on the nature of the set of variations and the set of admissible sections. The method of Lagrange multipliers is also applied for a deeper study of these constraints. PB Springer SN 0167-8019 YR 2012 FD 2012 LK https://hdl.handle.net/20.500.14352/43804 UL https://hdl.handle.net/20.500.14352/43804 LA eng NO Abraham, R., Marsden, J.E.: Foundations of Mechanics. Benjamin/Cummings Publishing, Advanced Book Program, Reading (1978)Anderson, I.M., Fels, M.E., Torre, C.: Group invariant solutions without transversality and the principle of symmetric criticality. In: Bäcklund and Darboux transformations. The Geometry of Solitons, Halifax, NS, 1999. CRM Proc. Lecture Notes, vol. 29, pp. 95–108. Am. Math. Soc., Providence (2001)Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edn. Graduate Texts in Mathematics, vol. 60. Springer, New York (1989)Castrillón López, M., García, P.L., Ratiu, T.: Euler-Poincaré reduction on principal bundles. Lett. Math. Phys. 58(2), 167–180 (2001)Castrillón, M., García, P.L., Rodrigo, C.: Euler-Poincaré reduction in principal fibre bundles and the problem of Lagrange. Differ. Geom. Appl. 25(6), 585–593 (2007)Castrillón López, M.,Marsden, J.: Some remarks on Lagrangian and Poisson reduction for field theories. J. Geom. Phys. 48(1), 52–83 (2003)Castrillón López, M., Muñoz Masqué, J.: The geometry of the bundle of connections. Math. Z. 236(4), 797–811 (2001)García, P.L.: The Poincaré-Cartan invariant in the calculus of variations. Symp. Math. 14, 219–246 (1974)Giachetta, G., Mangiarotti, L., Sarnanashvily, G.: New Lagrangian and Hamiltonian Methods in Field Theory. World Scientific, Singapore (1997)Goldschmidt, H., Sternberg, S.: The Hamiltonian-Cartan formalism in the calculus of variations. Ann. Inst. Fourier 23(1), 203–267 (1973)Kobayashi, S., Numizu, K.: Foundations of Differential Geometry, vol. I. Wiley-Interscience, New York (1963)Kobayashi, S., Numizu, K.: Foundations of Differential Geometry, vol. II.Wiley-Interscience, New York (1969)Marsden, J.E., Patrick, G., Shkoller, S.: Multisymplectic geometry, variational integrators, and nonlinear PDEs. Commun. Math. Phys. 199, 351–395 (1998)Marsden, J.E., Ratiu, T.S.: Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, 2nd edn. Texts in Applied Mathematics, vol. 17. Springer, New York (1999)Moser, J., Veselov, A.: Discrete versions of some classical integrable systems and factorization of matrix polynomials. Commun. Math. Phys. 139(2), 217–243 (1991)Saunders, D.J.: The Geometry of Jet Manifolds. Cambridge University Press, Cambridge (1989)Vankerschaver, J.: Euler-Poincaré reduction for discrete field theories. J. Math. Phys. 48(3) (2007) NO ICMAT (CSIC, UAM, UC3M, UCM), DS Docta Complutense RD 16 may 2024