Isometric Embeddings of Riemannian Manifolds

@inproceedings{Gnther2010IsometricEO,
  title={Isometric Embeddings of Riemannian Manifolds},
  author={Matthias G{\"u}nther},
  year={2010}
}
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 embedding. A further question is the regularity of the embedding in dependence on the regularity of… CONTINUE READING
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