Smooth isometric immersions of surfaces into \mathbb{R}^{4}

Every closed smooth Riemannian surface admits a smooth isometric immersion into ℝ⁴, resolving the closed-surface form of the four-dimensional isometric-immersion problem. This includes nonorientable surfaces and metrics of arbitrary Gaussian curvature. (Lean)

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Smooth isometric immersions of closed surfaces into Euclidean four-space

September 23, 2026 · source · cite as \cite{OAI:Smooth-isometric-immersions-of-closed-surfaces-into-Euclidean-four-space-September-23-2026}

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.

Result 333 · Differential geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.