Isometric embedding of a compact Riemannian manifold into Euclidean space

Abstract

An isometric immersion of an n n -dimensional compact Riemannian manifold with sectional curvature always less than λ − 2 {\lambda ^{ - 2}} into Euclidean space of dimension 2 n − 1 2n - 1 can never be contained in a ball of radius λ \lambda . This generalizes and includes results of Tompkins and Chern and Kuiper.