Counterexamples for Local Isometric Embedding
Differential Geometry
2007-05-23 v1 Analysis of PDEs
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.
Cite
@article{arxiv.math/0208127,
title = {Counterexamples for Local Isometric Embedding},
author = {Nikolai Nadirashvili and Yu Yuan},
journal= {arXiv preprint arXiv:math/0208127},
year = {2007}
}
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