Rigidity of spherical product Ricci solitons

Ao Sun; Jonathan J. Zhu

Rigidity of spherical product Ricci solitons

Differential Geometry 2023-03-29 v3

Authors: Ao Sun , Jonathan J. Zhu

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.

Keywords

ricci soliton rigidity shrinking soliton ricci flow einstein manifold clifford-type soliton mean curvature flow

Cite

@article{arxiv.2108.02326,
  title  = {Rigidity of spherical product Ricci solitons},
  author = {Ao Sun and Jonathan J. Zhu},
  journal= {arXiv preprint arXiv:2108.02326},
  year   = {2023}
}

Comments

34 pages; corrected a missing term before (4.5) which does not significantly affect the proof strategy

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