PreprintCC BY 4.0arXiv
Sphere Theorems for 10/3-Positive Curvature Operator of the Second Kind
Abstract
In this paper, we prove that every connected closed Riemannian manifold of dimension n≥4 with 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 10/3-nonnegative curvature operator of the second kind. The key step is to show that 10/3-positivity implies the PIC1 condition. Finally, we give an example showing that 10/3 is optimal for deducing PIC1 from α-positivity.
Related
- Some vanishing theorems on (p,q) double form and curvature operator of the second kind
- Sphere Theorems for Immersed Hypersurfaces with Constant Scalar Curvature
- Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere
- A Two-Stage Construction of Positive Curvature on the Gromoll-Meyer Sphere
- Positive sectional curvature on the exotic $8$-sphere and order-three homotopy $10$-spheres
BibTeX
@misc{cheng2026sphere,
title = {{Sphere Theorems for $\frac103$-Positive Curvature Operator of the Second Kind}},
author = {Haiqing Cheng and Kui Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26269},
eprint = {2610.26269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26269},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sphere Theorems for 10/3-Positive Curvature Operator of the Second Kind
AU - Haiqing Cheng
AU - Kui Wang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26269
UR - https://arxiv.org/abs/2610.26269
AB - In this paper, we prove that every connected closed Riemannian manifold of dimension n≥4 with 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 10/3-nonnegative curvature operator of the second kind. The key step is to show that 10/3-positivity implies the PIC1 condition. Finally, we give an example showing that 10/3 is optimal for deducing PIC1 from α-positivity.
ER -