Human action recognition based on RGB-D sequences is an important research direction in the field of computer vision. In this work, we incorporate the skeleton on the Grassmann manifold in order to model the human action as a trajectory. Given the couple of matched points on the Grassmann manifold, we introduce the special orthogonal group SO(3) to exploit the rotation ignored by the Grassmann manifold. In fact, our objective is to define the best weighted linear combination between distances in Grassmann and SO(3) man-ifolds according to the nature of action, while modeling human actions by temporal trajectories and finding the best weighted combination. The effectiveness of combining the two non-Euclidean spaces was validated on three standard challenging 3D human action recognition datasets (G3D-Gaming, UTD-MHAD multimodal action and Florence3D-Action), and the preliminary results confirm the accuracy of the proposed method comparatively to relevant methods from the state of the art.