The local moduli ofSasakian 3‐manifolds

The Newman‐Penrose‐Perjes formalism is applied to Sasakian 3‐manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian structure with scalar curvature equal to this function. The case where the scalar curvature is constant ( η ‐Einstein Sasakian metrics) is completely solved locally. The resulting Sasakian manifolds include S 3 , Nil, and , as well as the Berger spheres. It is also shown that a conformally flat Sasakian 3‐manifold is Einstein of positive scalar curvature.