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Preprint in the OpenAI Math release

A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric

OpenAI

Abstract

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.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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