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Geometrical aspects of the Landau-Hall problem on the hiperbolic plane.

A. López AlmoroxC. Tejero Prieto — 2001

RACSAM

Se discuten algunos aspectos del problema de Landau-Hall hiperbólico. El álgebra de Lie de las simetrías infinitesimales de este problema se da explícitamente, resultando ser isomorfa a so(2,1) y que sus invariantes Noether asociados son los momentos angulares hiperbólicos. Asimismo se desarrolla la formulación hamiltoniana, lo que nos permitirá obtener la variedad de órbitas de energía constante de este problema mediante técnicas de reducción simpléctica.

On the first secondary invariant of Molino's central sheaf

Jesús A. Álvarez López — 1996

Annales Polonici Mathematici

For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and other geometric properties are also proved to be equivalent to tautness.

On riemannian foliations with minimal leaves

Jesús A. Alvarez Lopez — 1990

Annales de l'institut Fourier

For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is 2 , a simple characterization of this geometrical property is proved.

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