This paper proposes Dual-SignLanguageNet (DSLNet) to address the challenge of Independent Sign Language Recognition (ISLR), which struggles to distinguish between morphologically similar but semantically distinct gestures. DSLNet employs a dual-reference, dual-stream architecture that models hand shape and movement trajectories in separate coordinate systems. It performs viewpoint-independent shape analysis using a wrist-centered coordinate system, and context-aware trajectory modeling using a face-centered coordinate system. It utilizes topology-aware graph convolution for shape analysis and a Finsler geometry-based encoder for trajectory modeling, and integrates the two streams via a geometry-based optimal transfer fusion mechanism. Experimental results demonstrate that DSLNet achieves accuracies of 93.70%, 89.97%, and 99.79% on the WLASL-100, WLASL-300, and LSA64 datasets, respectively, demonstrating state-of-the-art performance with significantly fewer parameters than competing models.