International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 2, Pages 117-127

The local moduli of Sasakian 3-manifolds

Brendan S. Guilfoyle

Mathematics Department, Institute of Technology Tralee, Clash, Tralee, Co. Kerry, Ireland

Received 16 February 2001

Copyright © 2002 Brendan S. Guilfoyle. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 S3, Nil, and SL˜2(), as well as the Berger spheres. It is also shown that a conformally flat Sasakian 3-manifold is Einstein of positive scalar curvature.