Family 358Differential geometryLeanNot yet digested
A three-manifold without conjugate points or nonpositive curvature
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.
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A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric
Sep 24, 2026·paper.pdfLean
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.