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The authors introduce a planar web on a 2-dimensional surface M as a special G -structure. The classical construction by W. Blaschke associates a connection to every planar web. The authors deduce that the Blaschke connection is the only natural onetexto impreso
Second-order Lagrangians depending on a surface which are parameter-invariant and also invariant under rigid motions of Euclidean 3-space are classified.texto impreso
The complex of s-horizontal forms of a smooth foliation F on a manifold M is proved to be exact for every s = 1, . . . , n = codim F, and the cohomology groups of the complex of its global sections, are introduced. They are then compared with ot[...]texto impreso
Let C be the bundle of connections of a principal G-bundle ?: P ? M,and let V be the vector bundle associated with P by a linear representation G ? GL(V ) on a finite-dimensional vector space V . The Lagrangians on J 1(C ×M V) whose current form[...]texto impreso
Castrillón López, Marco ; Gadea, P.M. ; Muñoz Masqué, Jaime | the American Romanian Academy of Arts and Sciences (USA) | 1999The paper is a survey of several results by the authors, the main one of them being the following characterization of homogeneous algebraic distributions: Let us consider a vertical distribution D on the vector bundle p:E?M locally spanned by ve[...]texto impreso
Let ?:P?M be a principal SU(2)-bundle, let autP [resp. gauP?autP] be the Lie algebra [resp. the ideal] of all G-invariant [resp. G-invariant ?-vertical] vector fields in X(P), and let p:C(P)?M be the bundle of connections of P. A differential fo[...]texto impreso
Let ?:P?M be a principal G-bundle. Then one can consider the following diagram of fibre bundles: \CD J^{1}(P) @> \pi_{10}> > P\\ @VqVV @VV\pi V\\ C(P) @> p> > M\endCD where p is the bundle of connections of ?. As is well known, q is also a pri[...]texto impreso
Given a principal bundle P?M we classify all first order Lagrangian densities on the bundle of connections associated to P that are invariant under the Lie algebra of infinitesimal automorphisms. These are shown to be variationally trivial and t[...]texto impreso
The structure of the algebra of gauge-invariant differential forms on the bundle C × ME is determined, where p:C?M is the bundle of connections of a U(1) principal bundle ? : P?M, and E?M is the associated bundle to P by the representation ?r, r[...]texto impreso
Let ?:P?M be a principal G-bundle. One denotes by J1P the 1-jet bundle of local sections of ?, by autP the Lie algebra of G-invariant vector fields of P and by gauP the ideal of ?-vertical vector fields in autP. A differential form ? on J1P is s[...]texto impreso
Let C ? M be the bundle of connections of a principal G-bundle P ? M over a pseudo-Riemannian manifold (M,g) of signature (n+, n?) and let E ? M be the associated bundle with P under a linear representation of G on a finite-dimensional vector sp[...]texto impreso
The paper presents some basic facts concerning the formulation of the gauge invariance property of the electromagnetic field in terms of differentiable manifolds. For example, the gauge potentials are identified as differential one-forms on the [...]texto impreso
The global inverse problem of the calculus of variations for the particular case of first-order quasi-linear PDEs is solved. Some examples in the field theory are discussed.texto impreso
Muñoz Masqué, Jaime ; Pozo Coronado, Luis Miguel | Natsional. Akad. Nauk Ukraïni, Inst. Mat., Kiev | 2000The authors use the procedure developed in [9] to develop a Hamiltonian structure into the variational problem given by the integral of the squared curvature on the spatial curves. The solutions of that problem are the elasticae or nonlinear spl[...]texto impreso
Let C?M be the bundle of connections of a principal bundle on M . The solutions to Hamilton–Cartan equations for a gauge-invariant Lagrangian density ? on C satisfying a weak condition of regularity, are shown to admit an affine fibre-bundle [...]
