On the mean curvature of Nash isometric embeddings

G. Pacelli Bessa; J. Fabio Montenegro

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arXiv · 0809.2563

On the mean curvature of Nash isometric embeddings

G. Pacelli Bessa·J. Fabio Montenegro

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Abstract

J. Nash proved that the geometry of any Riemannian manifold M imposes no restrictions to be embedded isometrically into a (fixed) ball B_{\mathbb{R}^{N}}(1) of the Euclidean space R^N. However, the geometry of M appears, to some extent, imposing restrictions on the mean curvature vector of the embedding.

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G. Pacelli Bessa, J. Fabio Montenegro. 2008-09-16. On the mean curvature of Nash isometric embeddings. https://arxiv.org/abs/0809.2563

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