Isometric Embedding of Riemannian Manifolds in Euclidean Spaces

Abstract

Isometric embedding of Riemannian manifolds: Fundamental theorems Surfaces in low dimensional Euclidean spaces Local isometric embedding of surfaces in $\mathbb{R}^3$: Basic equations Nonzero Gauss curvature Gauss curvature changing sign cleanly Nonnegative Gauss curvature Nonpositive Gauss curvature Global isometric embedding of surfaces in $\mathbb{R}^3$: Deformation of surfaces The Weyl problem Complete negatively curved surfaces Boundary value problems Bibliography Index.