%0 Journal Article
%T Extremal Sasakian Geometry on S^3-bundles over Riemann Surfaces
%A Charles P. Boyer
%A Christina W. T£¿nnesen-Friedman
%J Mathematics
%D 2013
%I arXiv
%X In this paper we study the Sasakian geometry on S^3-bundles over a Riemann surface of genus g>0 with emphasis on extremal Sasaki metrics. We prove the existence of a countably infinite number of inequivalent contact structures on the total space of such bundles that admit 2-dimensional Sasaki cones each with a Sasaki metric of constant scalar curvature (CSC). This CSC Sasaki metric is most often irregular. We further study the extremal subset in the Sasaki cone showing that if 0<g<5 it exhausts the entire cone. Examples are given where exhaustion fails.
%U http://arxiv.org/abs/1302.0776v1