nLab Grauert embedding theorem

Statement

Every real-analytic $n$-dimensional second countable Hausdorff manifold admits a real-analytic proper injective immersion into a euclidean space $\mathbf{R}^k$ of sufficiently high dimension.

Related concepts

• Whitney embedding theorem

• Narasimhan embedding theorem

• Nash embedding theorem

References

The original reference is Theorem 3 in

• Hans Grauert, On Levi’s Problem and the Imbedding of Real-Analytic Manifolds, Annals of Mathematics, Second Series, Vol. 68, No. 2 (Sep., 1958), pp. 460-472, doi.