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arXiv · 2108.02326

Rigidity of spherical product Ricci solitons

Ao Sun·Jonathan J. Zhu
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Abstract

We show that $S^2\times S^2$ is isolated as a shrinking Ricci soliton in the space of metrics, up to scaling and diffeomorphism. We also prove the same rigidity for $S^2\times N$, where $N$ belongs to a certain class of closed Einstein manifolds. These results are the Ricci flow analogues of our results for Clifford-type shrinking solitons for the mean curvature flow.

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Ao Sun, Jonathan J. Zhu. 2021-08-05. Rigidity of spherical product Ricci solitons. https://arxiv.org/abs/2108.02326

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