Biblioteca de la Universidad Complutense de Madrid

Euler-Poincare reduction in principal fibre bundles and the problem of Lagrange

Impacto

Castrillón López, Marco y Rodrigo, César y Garcia, Pedro L. (2007) Euler-Poincare reduction in principal fibre bundles and the problem of Lagrange. Differential Geometry and Its Applications, 25 (6). pp. 585-593. ISSN 0926-2245

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0926224507000435



Resumen

We compare Euler–Poincaré reduction in principal fibre bundles, as a constrained variational problem on the connections of
this fibre bundle and constraint defined by the vanishing of the curvature of the connection, with the corresponding problem of
Lagrange. Under certain cohomological condition we prove the equality of the sets of critical sections of both problems with the
one obtained by application of the Lagrange multiplier rule. We compute the corresponding Cartan form and characterise critical
sections as the set of holonomic solutions of the Cartan equation and, in particular, under a certain regularity condition for the
problem, we prove the holonomy of any solution of this equation.


Tipo de documento:Artículo
Palabras clave:Variational problems; problem of Lagrange; Lagrange multipliers; Euler-Poincare equations; Mathematics, Applied; Mathematics
Materias:Ciencias > Matemáticas > Geometría diferencial
Código ID:14875
Referencias:

M. Castrillón, T. Ratiu, S. Shkoller, Reduction in principal fiber bundles: Covariant Euler–Poincaré equations, Proc. Amer. Math. Soc. 128 (2000).

M. Castrillón, P.L. García, T.S. Ratiu, Euler–Poincaré reduction on principal bundles, Lett. Math. Phys. 58 (2) (2001) 167–180.

A. Fernández, P.L. García, C. Rodrigo, Stress-energy-momentum tensors in higher order variational calculus, J. Geom. Phys. 34 (1) (2000) 41–72.

A. Fernández, P.L. García, C. Rodrigo, Lagrangian reduction and constrained variational calculus, in: Proceedings of the IX Fall Workshop on Geometry and Physics, Vilanova i la Geltrú, 2000, Madrid, 2001, pp. 53–64. Publicaciones de la RSME 3.

P.L. García, Connections and 1-jet fiber bundles, Rend. Sem. Mat. Univ. Padova 47 (1972) 227–242.

P.L. García, J. Muñoz, Higher order regular variational problems, in: Symplectic geometry and mathematical physics, Aix-en-Provence, 1990, in: Progr. Math., vol. 99, Birkhäuser, Boston, 1991, pp. 136–159.

P.L. García, A. García, C. Rodrigo, Cartan forms for first order constrained variational problems, J. Geom. Phys. 56 (2006) 571–610.

Depositado:19 Abr 2012 08:32
Última Modificación:11 May 2016 14:10

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