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A family of non-collapsed steady Ricci solitons in even dimensions greater or equal to four
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abstract
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.
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Infinitely many non-collapsed steady Ricci solitons on complex line bundles
For each k at least 3, the complex line bundle O(k) over CP^{2m+1} admits infinitely many non-collapsed steady Ricci solitons, and for 3 ≤ k ≤ 2m+1 it admits an asymptotically conical Ricci-flat metric.
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