A family of steady Ricci solitons and Ricci-flat metrics
We produce new non-Kähler complete steady gradient Ricci solitons whose asymptotics combine those of the Bryant solitons and the Hamilton cigar. The underlying manifolds are of the form ℝ2 × M2 × ⋯ × Mr where Mi are arbitrary Einstein manifolds with positive scalar curvature. On the same spaces we also obtain a family of complete non-Kähler Ricci-flat metrics with asymptotically locally conical asymptotics. Among these new Ricci-flat and soliton examples are pairs with dimension 4m + 3 which are homeomorphic but not diffeomorphic.