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PreprintCC BY-SA 4.0arXiv

Positive biorthogonal curvature on S2× T2

  • Zhiqi Chen
  • Hui Zhang
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Abstract

We construct explicit Riemannian metrics with positive biorthogonal curvature on S2× T2, answering a question of Bettiol. In particular, positive biorthogonal curvature on a closed four-manifold does not force its fundamental group to be virtually free.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026positive,
  title = {{Positive biorthogonal curvature on $S^2\times T^2$}},
  author = {Zhiqi Chen and Hui Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08119},
  eprint = {2609.08119},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08119},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Positive biorthogonal curvature on S^2× T^2
AU  - Zhiqi Chen
AU  - Hui Zhang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08119
UR  - https://arxiv.org/abs/2609.08119
AB  - We construct explicit Riemannian metrics with positive biorthogonal curvature on S^2× T^2, answering a question of Bettiol. In particular, positive biorthogonal curvature on a closed four-manifold does not force its fundamental group to be virtually free.
ER  -