Learning from demonstration (LfD) has been increasingly used to encode robot tasks such that robots can achieve reproduction more flexibly in unstructured environments (e.g., households or factories). It is an effective alternative to preprogramming methods owing to its capacity of enabling robots to generalize to different situations. In this paper, we focus on LfD in the point-to-point movement case, where the dilemma of stability and accuracy exists. To avoid such a dilemma, we propose a learning approach that guarantees accuracy and stability simultaneously by means of constructed manifold immersion and submersion. We evaluate the proposed approach on two libraries of human handwriting motions (the LASA data set and a self-made GREEK data set) and on a set of experiments on the Barrett WAM robot.