The Local Isometric Embedding Problem for 3-Dimensional Riemannian Manifolds with Cleanly Vanishing Curvature

Abstract

We prove the following result: let (M, g) be a 3-dimensional C ∞ Riemannian manifold for which there exists a p ∈ M and a v ∈ T p M such that Then there exists a C ∞ isometric embedding from a neighborhood of p into ℝ6.