Existing temporal knowledge representation studies model real-world knowledge in a rigid manner, without considering the structural variations that emerge as temporal knowledge evolves. Specifically, for the same relation between different entities, the structures can be categorized as: 1) Homogeneous semantic knowledge structure; 2) Heterogeneous semantic knowledge structure. In fact, the semantic structural properties of relations among entities are not fixed but are determined by specific semantic context formed through interactions between entities and relations. These complex and variable inter-entity structures collectively reflect the underlying mechanisms of knowledge. To track them, we propose \(\text {LieT-H}^2\text {K}\) , a geometry-aware framework. This framework embeds each element of a fact into the Lie algebra space and lifts it to Lie group manifold, enabling high-dimensional modeling of knowledge and semantic information within Lie group space. Subsequently, \(\text {LieT-H}^2\text {K}\) employs group multiplication to construct deeply integrated interaction groups among entities, relations, and timestamps, facilitating the learning of multi-structured semantics over time. Finally, the learned multi-dimensional knowledge and semantic structures are mapped back to Lie algebra space via a logarithmic map, enabling optimization and semantic reasoning within a linearized and differentiable space. Extensive experiments on multiple benchmark datasets show that \(\text {LieT-H}^2\text {K}\) outperforms existing SOTA methods.