English

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.

Keywords

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}
}

Comments

submitted