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Besides the product of a positive Einstein manifold with the Euclidean Gaussian shrinker, does there exist other complete (nonconpact) gradient shrinking Ricci soliton with nonnegative Ricci curvature?

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  • $\begingroup$ Probably this is only known in dimension 3: see Theorem 1.1 in arxiv.org/pdf/0710.5579v3.pdf. Can you give some explanation as to why you're interested in solitons with (in particular) non-negative Ricci curvature? $\endgroup$ Apr 7, 2014 at 15:10
  • $\begingroup$ A interesting problem is the classification for shrinking Ricci solitons. There are examples of gradient shrinking Ricci soliton with undefinite Ricci curvature. So I want to get to some insight from different kinds of examples. $\endgroup$
    – Yiyan
    Apr 7, 2014 at 16:57
  • $\begingroup$ By Ni's result, $Ric\geq 0$ implies that $R>c$ for some positive constant. I'm not quite sure but it seems that all known examples have $R\to 0$. $\endgroup$ Apr 11, 2014 at 14:43
  • $\begingroup$ @Yiyan Could you please give me some references about shrinking (or steady) Ricci soliton with undefinite Ricci curvature? I am looking for an example. $\endgroup$
    – Onil90
    Jun 6, 2016 at 8:53

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