Manuel Barros

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We exhibit a criterion for a reduction of variables for WillmoreChen submanifolds in conformal classes associated with generalized KaluzaKlein metrics on flat principal fibre bundles. Our method relates the variational problem of Willmore-Chen with an elasticity functional defined for closed curves in the base space. The main ideas involve the extrinsic(More)
We exhibit a new method to find Willmore tori and Willmore-Chen submanifolds in spaces endowed with pseudo-Riemannian warped product metrics, whose fibres are homogeneous spaces. The chief points are the invariance of the involved variational problems with respect to the conformal changes of the metrics on the ambient spaces and the principle of symmetric(More)
We solve the variational problem associated with the total charge action on bounded domains in D = 2 background gravitational fields. The solutions of the field equations, stability and solitons are obtained holographically in terms of the massless spinning particles that evolve generating worldlines which play the role of boundaries. Moreover, we construct(More)
Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D = 3 space forms. The moduli spaces of trajectories are completely and explicitly determined using the Lancret program. The moduli subspaces of closed solitons in the three sphere are also(More)
We propose and study WCh-branes of M-theory and type IIA theory on backgrounds that are related by Hopf T-duality. The dynamics of these branes, with a reasonable degree of gauge symmetry, is reduced to that for particles that evolve somewhere along elastic worldlines. This constitutes an interesting holographic principle that allows us to determine moduli(More)
1. I n t r o d u c t i o n Physical systems such as vor tex f i laments in perfect fluids, one-d imens iona l classical con t inuum Heisenberg chains and elastic strings can be thought of as one-d imens iona l ex tended objects, the support o f which, their centerl ine, may be mathemat ica l ly mode led by * Corresponding author. Tel.: 34 68 364173; fax: 34(More)
Models describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D = 3 Lorentzian spacetimes with constant curvature. The moduli spaces of trajectories are completely and explicitly determined. Trajectories are Lancret curves including ordinary helices. To get(More)
We introduce the notion of Gauss-Landau-Hall magnetic field on a Riemannian surface. The corresponding Landau-Hall problem is shown to be equivalent to the dynamics of a massive boson. This allows one to view that problem as a globally stated, variational one. In this framework, flowlines appear as critical points of an action with density depending on the(More)