On Eta-Einstein Sasakian Geometry
  We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein structures on many different compact manifolds, including exotic spheres. We also relate these results to the existence of Einstein-Weyl structures. 
Charles P. Boyer, Krzysztof Galicki and Paola Matzeu