Before revision:  They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} is closed , i.e. M is a compact manifold without boundary . In this paper, we show that under the same conditions, the Riemannian metric of M^h approximates the Riemannian metric of M, ;
After revision:  They showed that the Manifold-MLS procedure approximates the original manifold with approximation order of O(h^{k M\in C^{k} is closed , i.e. M is a compact manifold without boundary ) the Riemannian metric of M^h approximates the Riemannian metric of M, ;