Counterexamples for Local Isometric Embedding

Details Counterexamples for Local Isometric Embedding Counterexamples for Local Isometric Embedding

2002-08-16

arxiv.org/abs/math/0208127v1

Mathematics

Differential Geometry

submitted

Scientific paper

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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