A family of non-collapsed steady Ricci solitons in even dimensions greater or equal to four

We construct a family of non-collapsed, non-K"ahler, non-Einstein steady Ricci solitons in even dimensions greater or equal to four. These solitons exist on complex line bundles over K"ahler-Einstein manifolds of positive scalar curvature. They include a four-dimensional $U(2)$-invariant, non-collapsed Riemannian steady soliton on each of the line bundles $O(k)$, $k>2$ of $\mathbb{C}{P}^1$. Finally, we find Taub-Nut like Ricci solitons and demonstrate a new proof for the existence of the Bryant soliton.