RNA sequencing consists in quantifying RNA molecules in a cell sample in order to determine the gene expression of the sample. Single-cell sequencing enables such information to be extracted at the level of each individual cell. In practice, the gene expression of one cell is displayed as a vector, each coordinate of which contains the expression level of a given gene. The variability in gene expression across the sample is the result of an underlying dynamic process. It is this process that we are interested in characterizing. However, since single-cell sequencing is a destructive technique, the stage in the process at which each cell was observed is not known. In order to recover the dynamic process, one needs then to arrange the cells according to their progression through the process, based on the analysis of the expression vectors. This is known as trajectory inference. Now, recent advances in single-cell sequencing enable the extraction of a second vector -- referred to as RNA velocity -- which determines the future change in gene expression in a cell. Eventually, the data is given as a discrete vector field in a Euclidean space of dimension the number of genes of interest. Now, under the assumption that the main process the cells undergo is differentiation, that is a branching process, then the expression vectors should be distributed along a tree. The trajectory inference problem is then exactly that of inferring this tree. Solving such a problem boils down to estimating the corresponding shortest path distance. To this end, we investigate metrics on the space of integral curves of the RNA velocity field.