N-dimensional sl ( 2 ) -coalgebra spaces with non-constant curvature
2007; Elsevier BV; Volume: 652; Issue: 5-6 Linguagem: Inglês
10.1016/j.physletb.2007.07.012
ISSN1873-2445
AutoresÁngel Ballesteros, Alberto Enciso, Francisco J. Herranz, O. Ragnisco,
Tópico(s)Advanced Differential Geometry Research
ResumoAn infinite family of ND spaces endowed with sl(2)-coalgebra symmetry is introduced. For all these spaces the geodesic flow is superintegrable, and the explicit form of their common set of integrals is obtained from the underlying sl(2)-coalgebra structure. In particular, ND spherically symmetric spaces with Euclidean signature are shown to be sl(2)-coalgebra spaces. As a byproduct of this construction we present ND generalizations of the classical Darboux surfaces, thus obtaining remarkable superintegrable ND spaces with non-constant curvature.
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