2001/02/02 by Brendan Guilfoyle, Brendan S. Guilfoyle · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematics #Moduli #Moduli space #Physics #Pure mathematics #math.DG #msc:53C25
paper · pdf · doi:10.1155/s0161171202006774
published as Int. J. Math. Sci. 32 (2002) 117-127 · 9 pages, RevTeX, no figures
arxiv created 2001/02/02 · openalex publication_date 2002/01/01 · openalex created_date 2016/06/24 · arxiv updated 2021/11/15 · openalex updated_date 2026/08/05
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 , as well as the Berger spheres. It is also shown that a conformally flat Sasakian 3‐manifold is Einstein of positive scalar curvature.