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A note on closed isometric embeddings

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Müller, Olaf
Date of publication of this fulltext: 14 Oct 2013 08:15


A famous theorem due to Nash ([3]) assures that every Riemannian manifold
can be embedded isometrically into some Euclidean space En. An interesting
question is whether for a complete manifold M we can find a closed isometric
embedding. This note gives the affirmative answer to this question asked to
the author by Paolo Piccione.

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