N=4 Superconformal Mechanics and the Potential Structure of AdS Spaces

The dynamics of an N=4 spinning particle in a curved background is described using the N=4 superfield formalism. The $SU(2{)}_{local}\times SU(2{)}_{global}$ N=4 superconformal symmetry of the particle action requires the background to be a real “K"ahler-like” manifold whose metric is generated by a sigma-model superpotential. The anti-de-Sitter spaces are shown to belong to this class of manifolds.