International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 2, Pages 117-127
doi:10.1155/S0161171202006774
The local moduli of
Sasakian 3-manifolds
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.
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.