<p>Domain adaptation (DA) seeks to mitigate distribution discrepancies between source and target domains, enabling models trained on labeled source data to generalize effectively to unlabeled target data. Existing DA approaches predominantly focus on global distribution alignment while largely overlooking the intrinsic local geometric structures of data manifolds, which are critical for learning discriminative and domain-invariant representations. To address this limitation, we propose a novel geometry-aware divergence criterion, termed Local Geometry Mean Divergence (LGMD). Unlike conventional global mean matching strategies such as Maximum Mean Discrepancy (MMD), LGMD explicitly models manifold local structures through adaptive neighborhood reconstruction and geometry-preserving kernel embeddings in a Reproducing Kernel Hilbert Space (RKHS). By replacing global mean embeddings with locally weighted manifold means, LGMD captures fine-grained structural discrepancies between domains. Extensive experiments on multiple benchmark datasets demonstrate that LGMD consistently achieves superior performance compared to state-of-the-art methods, validating its robustness capability for deep domain adaptation.</p>