Manifolds with PIC1 pinched curvature
Differential Geometry
2025-05-14 v3
Abstract
Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022, Lott 2019) that three-dimensional complete manifolds with non-negatively pinched Ricci curvature must be flat or compact, thus confirming a conjecture of Hamilton. In this paper we generalise our work on the existence of Ricci flows from non-compact pinched three-manifolds in order to prove a higher-dimensional analogue. We construct a solution to Ricci flow, for all time, starting with an arbitrary complete non-compact manifold that is PIC1 pinched. As an application we prove that any complete manifold of non-negative complex sectional curvature that is PIC1 pinched must be flat or compact.
Keywords
Cite
@article{arxiv.2211.07623,
title = {Manifolds with PIC1 pinched curvature},
author = {Man-Chun Lee and Peter M. Topping},
journal= {arXiv preprint arXiv:2211.07623},
year = {2025}
}
Comments
To appear, Geometry and Topology