{"id":"openai-math/Smooth-isometric-immersions-of-closed-surfaces-into-Euclidean-four-space","pdf":"https://github.com/openai/math/blob/main/preprints/Smooth-isometric-immersions-of-closed-surfaces-into-Euclidean-four-space-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Smooth-isometric-immersions-of-closed-surfaces-into-Euclidean-four-space-September-23-2026","tags":["differential-geometry","isometric-immersion","riemannian-geometry","embedding-problems"],"score":0,"title":"Smooth isometric immersions of closed surfaces into Euclidean four-space","domain":"Differential geometry","family":"333","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"Every closed smooth Riemannian surface admits a smooth isometric immersion into Euclidean four-space, without an orientability assumption. This resolves the closed-surface form of the classical four-dimensional isometric-immersion problem.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Smooth isometric immersions of surfaces into ℝ 4"}