Domain adaptation methods aim to assist tasks in a given target domain by using labeling information from a source domain. Domain-wise and class-wise alignments are commonly used as prerequisites for domain adaptation. However, sample-wise information is not fully utilized, which leads to unsatisfactory alignment results. In this study, we fully use sample-wise information from a geometric perspective to obtain a finer structure-preserving alignment. First, we use the smooth triplet loss to obtain a sample-wise alignment based on distribution adaptation. Then, we introduce a structure regularization term to perform domain adaptation to maintain the geometric structure of data, and use the intrinsic steepest descent algorithm to solve the optimization problem to ensure the structure of the solution space. Finally, we compare our approach with state-of-the-art metric learning and domain adaptation algorithms on datasets comprising natural images and medical information. Experimental results are presented to demonstrate the effectiveness of our proposed algorithm.