Abstract
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.
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