Counterexamples for Local Isometric Embedding
classification
🧮 math.DG
math.AP
keywords
curvaturegausscannotconstructcounterexamplesembeddedembeddingexcept
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We construct smooth metrics on 2-manifold with nonpositive Gauss curvature which cannot be (C^3) locally isometrically embedded in R^3. Moreover, the Gauss curvature of the metric can be made negative except for one point.
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