On the mean curvature of Nash isometric embeddings
Differential Geometry
2008-09-16 v2
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.
Cite
@article{arxiv.0809.2563,
title = {On the mean curvature of Nash isometric embeddings},
author = {G. Pacelli Bessa and J. Fabio Montenegro},
journal= {arXiv preprint arXiv:0809.2563},
year = {2008}
}
Comments
A note of two pages