Multivariate functional data are generated by a system involving dynamic parameters depending on continuous variables. Outlier detection must consider both the individual behavior of the parameters and the dynamic correlation between them. Recent work has focused on multivariate functional depth. These approaches fail when the outlyingness is manifested in the shape of the curve rather than in its magnitude. This paper, based on our publication in the journal KBS Lejeune et al. (2020) presents the results of a new method in which outlying features are captured based on mapping functions from differential geometry. Experimental study on real and synthetic datasets and comparison with functional depth-based methods show that the proposed method combined with the latest outlier detection algorithms can be more effective. It is effective regardless of the proportion of outliers.