Multivariate functional data refer to a population of multivariate functions generated by a system involving dynamic parameters depending on continuous variables (e.g., multivariate time series). Outlier detection in such a context is a challenging problem because both the individual behavior of the parameters and the dynamic correlation between them are important. To address this problem, recent work has focused on multivariate functional depth to identify the outliers in a given dataset. However, most previous approaches fail when the outlyingness manifests itself in curve shape rather than curve magnitude. In this paper, we propose identifying outliers in multivariate functional data by a method whereby different outlying features are captured based on mapping functions from differential geometry. In this regard, we extract shape features reflecting the outlyingness of a curve with a high degree of interpretability. We conduct an experimental study on real and synthetic data sets and compare the proposed method with functional-depth-based methods. The results demonstrate that the proposed method, combined with state-of-the-art outlier detection algorithms, can outperform the functional-depth-based methods. Moreover, in contrast with the baseline methods, it is efficient regardless of the proportion of outliers.