Self-Dual Manifolds with Positive Ricci Curvature
  We prove that the connected sums CP_2 # CP_2 and CP_2 # CP_2 # CP_2 admit self-dual metrics with positive Ricci curvature. Moreover, every self-dual metric of positive scalar curvature on CP_2 # CP_2 is conformal to a metric with positive Ricci curvature. 
Claude LeBrun, Shin Nayatani, and Takashi Nitta