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

Ballesteros, Angel; Enciso, Alberto; Herranz, Francisco J.; Ragnisco, Orlando

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

Authors

Ballesteros, Angel

Enciso, Alberto

Herranz, Francisco J.

Ragnisco, Orlando

Description

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