OpenAI research collection · 1 manuscript · Source checked 2026-10-19
Every closed smooth Riemannian surface admits a smooth isometric immersion into ℝ^(4), resolving the closed-surface form of the four-dimensional isometric-immersion problem. This includes nonorientable surfaces and metrics of arbitrary Gaussian curvature.
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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.
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