Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shrinking Ricci solitons with positive isotropic curvature   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 $S^{n-1} \times \mathbb{R}$.

9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an