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Metrics with positive Ricci eigenvalue sums on πkΓ πm
Abstract
We construct metrics with k-positive Ricci curvature on πkΓ πm, for k,mβ₯2, 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.
Related
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BibTeX
@misc{chen2026metrics,
title = {{Metrics with positive Ricci eigenvalue sums on $\mathbbT^k\times \mathbbS^m$}},
author = {Huibin Chen and Yiyue Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15814},
eprint = {2609.15814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15814},
}
RIS
TY - UNPB
TI - Metrics with positive Ricci eigenvalue sums on π^kΓ π^m
AU - Huibin Chen
AU - Yiyue Zhang
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15814
UR - https://arxiv.org/abs/2609.15814
AB - We construct metrics with k-positive Ricci curvature on π^kΓ π^m, for k,mβ₯2, 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.
ER -