Year: 2026
Type: preprint
Abstract: In this paper, we prove that every connected closed Riemannian manifold of dimension $n\geq4$ with $\frac{10}{3}$-positive curvature operator of the second kind is diffeomorphic to a spherical space form. We also obtain a classification of connected closed Riemannian manifolds with $\frac{10}{3}$-nonnegative curvature operator of the second kind. The key step is to show that $\frac{10}{3}$-positivity implies the PIC1 condition. Finally, we give an example showing that $\frac{10}{3}$ is optimal for deducing PIC1 from $α$-positivity.
Source: arXiv (Cornell University)
Authors: Cheng, Haiqing, Wang, Kui
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223004070