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The Local Moduli of Sasakian 3-Manifolds

Brendan S. Guilfoyle
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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 ($\eta$-Einstein Sasakian metrics) is completely solved locally. The resulting Sasakian manifolds include $S^3$, $Nil$ and $\tilde{SL_2R}$, 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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Brendan S. Guilfoyle. 2001-02-02. The Local Moduli of Sasakian 3-Manifolds. https://doi.org/10.1155/s0161171202006774

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