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We present a theorem of Lancret for general helices in a 3-dimensional real-space-form which gives a relevant difference between hyperbolic and spherical geometries. Then we study two classical problems for general helices in the 3-sphere: the problem of solving natural equations and the closed curve problem.

- MANUEL BARROS, MIGUEL A. MEROÑO
- 2000

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)

- Manuel Barros, Miguel A. Meroiio
- 2003

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)

- Manuel Barros
- 2002

The simplest models describing spinning particles with rigidity, both massive and massless, are reconsidered. The moduli spaces of solutions are completely exhibited in backgrounds with constant curvature. While spinning massive particles can evolve fully along helices in any three-dimensional background, spinning massless particles need anti De Sitter… (More)

- Josu Arroyo, Manuel Barros, Oscar J.Garay
- 2008

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)

- Manuel Barros
- 2000

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)