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

Abstract

We construct a family of non-collapsed, non-Kähler, non-Einstein steady Ricci solitons in even dimensions greater or equal to four. These solitons exist on complex line bundles over Kähler-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.

Fixed gap in proof of Lemma 6.7 of previous version; general editing and additional explanations

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