This paper proposes Dual-SignLanguageNet (DSLNet) to address the challenge of Independent Sign Language Recognition (ISLR), which challenges recognizing morphologically similar but semantically distinct sign language gestures. DSLNet employs a dual-reference, dual-stream architecture that models hand shape and movement trajectories in separate coordinate systems. It models shape in wrist-centered coordinates and context-sensitive trajectories in face-centered coordinates, extracting their respective features using topology-aware graph convolution and a Finsler geometry-based encoder. Finally, the two features are integrated using a geometry-driven optimal transport fusion mechanism. Experimental results demonstrate that DSLNet achieves state-of-the-art performance (93.70%, 89.97%, and 99.79%, respectively) on the WLASL-100, WLASL-300, and LSA64 datasets with fewer parameters than competing models.