{"id":"openai-math/Zero-Plane-Rigidity-for-Einstein-Four-Manifolds","pdf":"https://github.com/openai/math/blob/main/preprints/Zero-Plane-Rigidity-for-Einstein-Four-Manifolds-October-4-2026/einstein-boundary.pdf","url":"https://github.com/openai/math/tree/main/preprints/Zero-Plane-Rigidity-for-Einstein-Four-Manifolds-October-4-2026","tags":["riemannian-geometry","einstein-manifolds","curvature"],"score":0,"title":"Zero-Plane Rigidity for Einstein Four-Manifolds","domain":"Differential geometry","family":"348","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We prove that a closed Einstein four-manifold with positive Einstein constant, nonnegative sectional curvature, and a zero-curvature plane has universal Riemannian cover isometric to a product of two round two-spheres. Under the normalization $`\\mathop{\\mathrm{Ric}}\\nolimits =3g`$, both spheres have radius $`1/\\sqrt3`$. The proof extends coupled estimates for the two Weyl curvature blocks to the boundary of the sectional-curvature cone and determines their equality case.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-04","reactions":{},"formalized":false,"family_title":"Nonnegative-curvature Einstein classification and an L 2 topological gap"}