Following a brief introduction t 3+1 Electrodynamics in curved space-time, the nature of the constraint equation that arises in the study of a force free,
axis-symmetric, stationary magnetosphere will be discussed. The relevance of the streaming function Omega and the nature of “poloidal surfaces”
will be developed from a geometric point of view. Finally we shall present an analytic solution to the constraint equation and discuss its physical properties.