{"id":"openai-math/Positively-curved-Einstein-four-manifolds","pdf":"https://github.com/openai/math/blob/main/preprints/Positively-curved-Einstein-four-manifolds-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Positively-curved-Einstein-four-manifolds-September-23-2026","tags":["riemannian-geometry","einstein-manifolds","classification"],"score":0,"title":"Positively curved Einstein four-manifolds","domain":"Differential geometry","family":"348","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We prove the classification conjecture for connected smooth closed Einstein four-manifolds with strictly positive sectional curvature. Up to positive scaling and isometry, every such manifold is the round four-sphere, the complex projective plane with its Fubini–Study metric, or real projective four-space with its round metric. No orientability assumption is needed.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Nonnegative-curvature Einstein classification and an L 2 topological gap"}