Recently introduced cost-effective depth sensors coupled with the real-time skeleton estimation algorithm of Shotton et al. [16] have resulted in a renewed interest in skeleton-based human action recognition. Most of the earlier skeleton-based approaches used either the joint locations or the joint angles to represent a human skeleton. In this paper, we propose a new skeletal representation that explicitly models the 3D geometric relationships between various body parts using rotations and translations in 3D space. Since 3D rigid body motions are members of the special Euclidean group SE(3), the proposed skeletal representation lies in the Lie group SE(3)×. . .×SE(3), which is a curved manifold. With the proposed representation human actions can be modeled as curves in this Lie group. Since classification of curves in this Lie group is not an easy task, we map the action curves from the Lie group to its Lie algebra, which is a vector space. We then perform classification using a combination of dynamic time warping, Fourier temporal pyramid representation and linear SVM. Experimental results on three action datasets show that the proposed representation performs better than various other commonly-used skeletal representations. The proposed approach also outperforms various state-of-the-art skeleton-based human action recognition approaches.