Isometric Embedding of a Compact Riemannian Manifold into Euclidean Space
Howard Jacobowitz · Proceedings of the American Mathematical Society · 1973
An isometric immersion of an $n$-dimensional compact Riemannian manifold with sectional curvature always less than ${\lambda ^{ - 2}}$ into Euclidean space of dimension $2n - 1$ can never be contained in a ball of radius $\lambda$. This generalizes and includes results of Tompkins and Chern and Kuiper.