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arXiv · 2111.12807

$SU(2)$-invariant steady gradient Ricci solitons on four-manifolds

Timothy Buttsworth
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Abstract

Using center manifolds and topological degree theory, we construct a new family of complete, $SU(2)$-invariant and steady gradient Ricci solitons on the four-dimensional non-compact cohomogeneity one manifold with group diagram $\mathbb{Z}_4\subset U(1)\subset SU(2)$. We also provide simpler constructions of the existing $U(2)$-invariant steady and complete gradient solitons on the cohomogeneity one manifolds with group diagrams $\mathbb{Z}_n\subset U(1)\subset SU(2)$ for any $n\in \mathbb{N}$, including Appleton's non-collapsed solitons for $n\ge 3$.

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Timothy Buttsworth. 2021-11-24. $SU(2)$-invariant steady gradient Ricci solitons on four-manifolds. https://arxiv.org/abs/2111.12807

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