On the mean curvature of Nash isometric embeddings

Details On the mean curvature of Nash isometric embeddings On the mean curvature of Nash isometric embeddings

2008-09-15

arxiv.org/abs/0809.2563v2

Mathematics

Differential Geometry

A note of two pages

Scientific paper

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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