Counterexamples for Local Isometric Embedding

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.

submitted

Cited by in corpus (2)

• Embedding of the Kerr-Newman Black Hole Surface in Euclidean Space
• Quasi-isometric embedding of Kerr poloidal sub-manifolds