Work

Metrics with positive Ricci eigenvalue sums on $\mathbb{T}^k\times \mathbb{S}^m$

Year: 2026

Type: preprint

Abstract: We construct metrics with $k$-positive Ricci curvature on $\mathbb{T}^k\times \mathbb{S}^m$, for $k,m\geq2$, arbitrarily close to the standard flat-round product in the smooth topology. The two-torus case disproves Wolfson's conjecture that every closed manifold with two-positive Ricci curvature has virtually free fundamental group. We also establish a local obstruction to two-positive Ricci curvature near closed backgrounds carrying three orthonormal parallel one-forms.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.15814

Authors: Chen, Huibin, Zhang, Yiyue

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213361371

Cites: 10

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Related to: 10