The local moduli of Sasakian 3 -manifolds

Brendan S. Guilfoyle

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 32, 1-11

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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:296101

DOI: 10.1155/S0161171202006774

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