On the mean curvature of Nash isometric embeddings

2008/09/15 by G. Pacelli Bessa, Bessa, G. Pacelli, J. Fabio Montenegro +1
Mathematics · #53C40 #53C42 #58C40 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C40 #msc:53C42 #msc:58C40

paper · pdf · doi:10.48550/arxiv.0809.2563

A note of two pages

arxiv created 2008/09/16 · arxiv updated 2009/12/01

Abstract

J. Nash proved that the geometry of any Riemannian manifold M imposes no restrictions to be embedded isometrically into a (fixed) ball B_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.

Related

• A note on closed isometric embeddings
• On the geometry of Riemannian isometric embeddings
• On the complexity of isometric immersions of hyperbolic spaces in any codimension
• Gunther's proof of Nash's isometric embedding theorem
• Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces