{"id":"openai-math/A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric","pdf":"https://github.com/openai/math/blob/main/preprints/A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Three-Manifold-Without-Conjugate-Points-and-Without-a-Nonpositively-Curved-Metric-September-24-2026","tags":["riemannian-geometry","3-manifolds","conjugate-points"],"score":0,"title":"A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric","domain":"Differential geometry","family":"358","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"A three-manifold without conjugate points or nonpositive curvature"}