N-dimensional sl(2)-coalgebra spaces with non-constant curvature

Details N-dimensional sl(2)-coalgebra spaces with non-constant curvature N-dimensional sl(2)-coalgebra spaces with non-constant curvature

2007-04-11

arxiv.org/abs/0704.1470v2

Phys.Lett.B652:376-383,2007

Physics

High Energy Physics

High Energy Physics - Theory

11 pages. Comments and new references have been added; expressions for scalar curvatures have been corrected and simplified

Scientific paper

10.1016/j.physletb.2007.07.012

An 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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