Counterexamples for Local Isometric Embedding
微分几何
2007-05-23 v1 偏微分方程分析
摘要
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.
引用
@article{arxiv.math/0208127,
title = {Counterexamples for Local Isometric Embedding},
author = {Nikolai Nadirashvili and Yu Yuan},
journal= {arXiv preprint arXiv:math/0208127},
year = {2007}
}
备注
submitted