Family 333Differential geometryNo LeanNot yet digested
Smooth isometric immersions of surfaces into ℝ
Every closed smooth Riemannian surface admits a smooth isometric immersion into ℝ, 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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Smooth isometric immersions of closed surfaces into Euclidean four-space
Sep 23, 2026·paper.pdf
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.