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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
- 1995

- 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)

- 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)

The purpose of this paper is to find out explicit solutions of the Betchov-Da Rios soliton equation in three-dimensional Lorentzian space forms. We start with non-null curves and obtain solutions living in certain fiat ruled surfaces in ~_3 and H~, as well as in ~3 and ~3. Next we take a null curve and have got solutions lying in the associated B-scrolls in… (More)

- MANUEL BARROS, MIGUEL A. MEROÑO
- 2000

We exhibit a criterion for a reduction of variables for Willmore-Chen submanifolds in conformal classes associated with generalized Kaluza-Klein metrics on flat principal fibre bundles. Our method relates the vari-ational problem of Willmore-Chen with an elasticity functional defined for closed curves in the base space. The main ideas involve the extrinsic… (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)

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 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 world-lines which play the role of boundaries. Moreover, we… (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)