The Geometric Structure of the B-Spline Manifolds

In the present paper, the geometric structure of the B-spline manifolds, which consists of all the B-spline functions, is given. From the definition of the B-spline manifolds of all the B-spline functions, it can be seen that the B-spline manifolds are ±1-flat. Moreover, the curvature tensor and the Gaussian curvature for two dimensional B-spline manifolds are obtained. At last, an example illustrates the validity of the Gaussian curvature obtained in this paper.