PreprintCC0arXiv
A Metric with Positive Sectional Curvature on S3× S3
Abstract
We construct a smooth Riemannian metric with strictly positive sectional curvature on S3× S3. Since S3× S3 is even-dimensional and has Euler characteristic zero, our result disproves the positive-curvature case of Hopf's sign conjecture. The metric and the proof were discovered by the Odin Automatic AI Research Agent.
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BibTeX
@misc{guo2026metric,
title = {{A Metric with Positive Sectional Curvature on $S^3\times S^3$}},
author = {Shengtao Guo and Ethan X. Fang and Junwei Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11980},
eprint = {2609.11980},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11980},
note = {CC0},
}
RIS
TY - UNPB
TI - A Metric with Positive Sectional Curvature on S^3× S^3
AU - Shengtao Guo
AU - Ethan X. Fang
AU - Junwei Lu
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.11980
UR - https://arxiv.org/abs/2609.11980
AB - We construct a smooth Riemannian metric with strictly positive sectional curvature on S^3× S^3. Since S^3× S^3 is even-dimensional and has Euler characteristic zero, our result disproves the positive-curvature case of Hopf's sign conjecture. The metric and the proof were discovered by the Odin Automatic AI Research Agent.
ER -