Given a compact Kähler manifold with positive holomorphic line bundle it follows from Tian's approximation theorem that the sequence of Fubini-Study forms induced by the Kodaira embeddings converges to the curvature of the line bundle. In this talk we consider a compact embeddable strongly pseudoconvex CR manifold of hypersurface type and a sequence of Kodaira maps associated to eigenfunctions of CR Toeplitz operators. I will present a CR version of Tian's approximation theorem that relates the Levi form of the underlying manifold to those of Sasakian spheres in complex Euclidean space. This is a joint work with Chin-Yu Hsiao, George Marinescu and Wei-Chuan Shen.
