Isometric immersion of flat Riemannian manifolds in Euclidean space.

Isometric Embeddings of Riemannian Manifolds

The dot in (1) denotes the usual scalar product of R. The notion embedding means, that w is locally an immersion and globally a homeomorphism of M onto the subspace u(M) of R*. If an embedding w : M -• R satisfies (1) on the whole M, we speak of an isometric embedding. If w is an immersion and a solution of (1) in a (possibly small) neighbourhood of any point of M, we speak of a local isometric...

Isometric Embedding of Riemannian Manifolds

Flat Homogeneous Pseudo-Riemannian Manifolds

The complete homogeneous pseudo-Riemannian manifolds of constant non-zero curvature were classified up to isometry in 1961 [1]. In the same year, a structure theory [2] was developed for complete fiat homogeneous pseudo-Riemannian manifolds. Here that structure theory is sharpened to a classification. This completes the classification of complete homogeneous pseudo-Riemannian manifolds of arbit...

Relative Isometric Embeddings of Riemannian Manifolds

We prove the existence of C1 isometric embeddings, and C∞ approximate isometric embeddings, of Riemannian manifolds into Euclidean space with prescribed values in a neighborhood of a point.

RELATIVE ISOMETRIC EMBEDDINGS OF RIEMANNIAN MANIFOLDS IN Rn

We prove the existence of C isometric embeddings, and C∞ approximate isometric embeddings, of Riemannian manifolds into Euclidean space with prescribed values in a neighborhood of a point.