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 SL˜ 2 (ℝ), as well as the Berger spheres. It
is also shown that a conformally flat Sasakian 3-manifold is Einstein of positive scalar curvature.