The consistency training (CT)-based semi-supervised learning (SSL) bites state-of-the-art performance on SSL-based image classification. However, the existing CT-based SSL methods do not highlight the non-Euclidean characteristics and class-wise varieties of embedding spaces in an SSL model, thus they cannot fully utilize the effectiveness of CT. Thus, we propose a metric tensor-based consistency regularization, exploiting the class-variant geometrical structure of embeddings on the high-dimensional feature space. The proposed method not only minimizes the prediction discrepancy between different views of a given image but also estimates the intrinsic geometric curvature of embedding spaces by employing the global and local metric tensors. The global metric tensor is used to globally estimate the class-invariant embeddings from the whole data distribution while the local metric tensor is exploited to estimate the class-variant embeddings of each cluster. The two metric tensors are optimized by the consistency regularization based on the weak and strong augmentation strategy. The proposed method provides the highest classification accuracy on average compared to the existing state-of-the-art SSL methods on conventional datasets.