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Counterexamples for Local Isometric Embedding

Nikolai Nadirashvili·Yu Yuan
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Abstract

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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Nikolai Nadirashvili, Yu Yuan. 2002-08-16. Counterexamples for Local Isometric Embedding. https://arxiv.org/abs/math/0208127

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