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Autor Castrillón López, Marco |
Documentos disponibles escritos por este autor (60)
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Castrillón López, Marco ; Valdés Morales, Antonio | 2001-05We show that projectively invariant evolution operators have unavoidable singularities. In particular, we see that there exists no non-singular projective evolution operator well-defined over straight lines nor conics.texto impreso
A general reduction theory for field theoretical Lagrangians on principal fiber bundles is presented. The reduced variational problem as well as the associated equations are formulated. The link between the solutions of the original problem and [...]texto impreso
Castrillón López, Marco ; Ratiu, Tudor S. ; Shkoller, Steve | American Mathematical Society | 1999-11-01In Lagrangian mechanics the simplest example of reduction is the Euler-Poincaré reduction. In this case, the configuration space is a Lie group G and the Lagrangian function L:TG?R is invariant under the natural action of the group on TG by righ[...]texto impreso
Basic results on gauge invariance of differential forms on the bundle of connections of an arbitrary principal U(1)-bundle and its associated bundles, are reviewed in terms of the underlying geometry to such bundles, within the framework of clas[...]texto impreso
This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian L or the momentum map J[...]texto impreso
Given a Hamiltonian system on a fiber bundle, the Poisson covariant formulation of the Hamilton equations is described. When the fiber bundle is a G-principal bundle and the Hamiltonian density is G-invariant, the reduction of this formulation i[...]texto impreso
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We study the class K2+K4 of homogeneous pseudo-Kähler structures in the strongly degenerate case. The local form and the holonomy of a pseudo-Kähler manifold admitting such a structure are obtained, leading to a possible complex generalization o[...]texto impreso
We prove that on the bundle of connections of an arbitrary principal bundle ?: P ? M there exists a canonical differential 2--form taking values in the adjoint bundle ;ing: adg:: ad P ? M which defines a generalized symplectic structure and whic[...]texto impreso
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An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger’[...]texto impreso
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanheck[...]texto impreso
The total curvature of C2 curves embedded in an arbitrary Riemannian manifold is shown to be the limit of the curvatures of inscribed geodesic polygons. The formula for the total curvature of a curve as the least upper bound of curvatures of ins[...]texto impreso
Castrillón López, Marco ; Muñoz Masqué, Jaime ; Ratiu, T.S. | Institute of Mathematics and Informatics | 2001Let ?:P?M be a principal G-bundle and p:C?M the bundle of connections on ?. In the present paper the authors study variational problems defined by Lagrangians L:J1C?R. The starting point is the classical theorem of Utiyama which characterizes th[...]texto impreso
Lagrangians are investigated which are defined on the product of the cotangent bundle of a manifold and a vector space, where the vector space is the representation space of a linear representation of the group U(1) as the gauge group. It is sho[...]