Differential geometry·OpenAI Math·Result 358·Lean formalisation listed
A three-manifold without conjugate points or nonpositive curvature
One of the 372 results in OpenAI's public mathematics catalogue, filed under differential geometry: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric
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What OpenAI claims
Constructs a closed connected orientable smooth three-manifold that admits a metric without conjugate points but no metric of nonpositive sectional curvature. This answers negatively, already in dimension three, whether the first metric-existence property implies the second. (Lean)
Paper
A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric
We construct a closed connected orientable smooth three-manifold that admits a smooth Riemannian metric without conjugate points but admits no smooth Riemannian metric of nonpositive sectional curvature.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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