Shrinking Ricci solitons with positive isotropic curvature

Keaton Naff

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arXiv · 1905.10305

Shrinking Ricci solitons with positive isotropic curvature

Keaton Naff

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Abstract

We show that in dimensions $n \geq 12$, 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 $n \geq 5$, 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 $S^{n-1} \times \mathbb{R}$.

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BibTeX RIS

Keaton Naff. 2019-05-29. Shrinking Ricci solitons with positive isotropic curvature. https://arxiv.org/abs/1905.10305

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