Shrinking Ricci solitons with positive isotropic curvature

Abstract

We show that in dimensions $n\ge 12$, a non-flat complete gradient shrinking solitons with uniformly positive isotropic curvature (PIC) must be a quotient of either the round sphere $S^n$ or the cylinder $S^{n-1}\times \mathbb{R}$. We also observe that in dimensions $n\ge 5$, a complete gradient shrinking soliton that is strictly PIC and weakly PIC2 must be a quotient of either the round sphere $S^n$ or the cylinder $S^{n-1}\times \mathbb{R}$.

Citations updated

References in corpus (1)

• Kähler-Ricci Shrinkers and Ancient Solutions with Nonnegative Orthogonal Bisectional Curvature

Cited by in corpus (1)

• Ancient solutions to the Ricci flow with isotropic curvature conditions