Extremal Sasakian Geometry on $T^2\times S^3$ and Related Manifolds
  We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on $T^2\times S^3$ and certain related manifolds. These structures occur in bouquets and exhaust the Sasaki cones in all except one case in which there are no extremal metrics. 
Charles P. Boyer and Christina W. T{\o}nnesen-Friedman
math.DG