Some isometric embedding and rigidity results for Riemannian manifolds

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In this note, we announce some new results concerning rigidity and isometric embeddings of Riemannian manifolds. A special case of the main result states that a general Mn [unk] Rn+r, r≤(n - 1)(n - 2)/2, is uniquely determined up to finitely many constants by its induced ds2.

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