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Autor Muñoz Masqué, Jaime |
Documentos disponibles escritos por este autor (35)
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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 one![]()
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Second-order Lagrangians depending on a surface which are parameter-invariant and also invariant under rigid motions of Euclidean 3-space are classified.![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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.![]()
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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[...]![]()
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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 [...]![]()
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Higher-order Lagrangians on T*(M) invariant under the natural representation of gauge fields of M x U(1) on the cotangent bundle are determined.![]()
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Let p:E?M be a vector bundle of dimension n+m and (x?,yi), ?=1,…,n, i=1,…,m, be fibre coordinates. A vertical vector field X on E is said to be algebraic [respectively, algebraic homogeneous of degree d] if its coordinate expression is of the ty[...]![]()
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It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton- Cartan equations of these Lagrangians are obtained and proved to be also [...]![]()
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We summarize und analyze several results concerning the variational character of a set of first order quasi-linear PDEs. A local characterization of the problem is given, and the global obstructions to the problem are obtained.![]()
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Let M be a smooth oriented connected n-dimensional manifold and let M be the space of pseudo-Riemannian metrics on M of a given signature (n+,n?),n++n?=n> 1. A system of n metric invariants is attached to each metric in M, called the Ricci invar[...]![]()
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Let P ? M be a principal G-bundle over a pseudo-Riemannian manifold (M, g). If G is semisimple, the Euler-Lagrange and the Hamilton-Cartan equations of the Yang-Mills Lagrangian defined by g are proved to remain unchanged if the Cartan-Killing m[...]![]()
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The moduli space of jets of G-structures admitting a canonical linear connection is shown to be isomorphic to the quotient by G of a natural G-module.![]()
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The deparametrization problem for parameter-invariant Lagrangian densities defined over J(1)(N, F), is solved in terms of a projection onto a suitable jet bundle. The Hamilton-Cartan formalism for such Lagrangians is then introduced and the pre-[...]![]()
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A projection is defined such that a second-order Lagrangian density factors through this projection module contact forms if and only if it is parameter invariant. In this way, a geometric interpretation of the parameter invariance conditions is [...]![]()
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The notion of a projective parallelism either on a differentiable or on a complex analytic manifold $M$ is introduced and its topological invariants and cohomological obstructions are studied. In the complex case a canonical linear connection is[...]