N-dimensional sl(2)-coalgebra spaces with non-constant curvature
High Energy Physics - Theory
2008-11-26 v2 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.0704.1470,
title = {N-dimensional sl(2)-coalgebra spaces with non-constant curvature},
author = {Angel Ballesteros and Alberto Enciso and Francisco J. Herranz and Orlando Ragnisco},
journal= {arXiv preprint arXiv:0704.1470},
year = {2008}
}
Comments
11 pages. Comments and new references have been added; expressions for scalar curvatures have been corrected and simplified