The Local Moduli of Sasakian 3-Manifolds

Authors

Brendan Guilfoyle, School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, Co. Kerry, Ireland.Follow

ORCID

0000-0002-7437-5046

Document Type

Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Disciplines

Mathematics | Physical Sciences and Mathematics

Publication Details

International Journal of Mathematics and Mathematical Sciences, vol. 2002.

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.

Recommended Citation

The local moduli of Sasakian 3-manifolds, Brendan S. Guilfoyle, International Journal of Mathematics and Mathematical Sciences, vol. 32, 296101, https://doi.org/10.1155/S0161171202006774