Four-dimensional cohomogeneity one Ricci flow and nonnegative sectional curvature

TL;DR

This paper presents the first known examples of closed 4-manifolds with nonnegative sectional curvature that do not preserve this curvature condition under Ricci flow evolution.

Contribution

It provides the first explicit examples of 4-manifolds with nonnegative sectional curvature that lose this property during Ricci flow, highlighting limitations of curvature preservation.

Findings

First examples of 4-manifolds with nonnegative sectional curvature losing this property under Ricci flow

Demonstrates that nonnegative sectional curvature is not preserved in certain Ricci flows for 4-manifolds

Highlights new phenomena in the behavior of curvature under Ricci flow in four dimensions

Abstract

We exhibit the first examples of closed 4-manifolds with nonnegative sectional curvature that lose this property when evolved via Ricci flow.