Invariants of Riemannian curves in dimensions 2 and 3

In this article, a complete and geometrical description of minimal sets of differential invariants in 2- and 3-dimensional Riemannian manifolds is given in terms of the dimension of the isometry group. These invariants provide a solution to the (local) problem of congruence of curves so that a final generalization of Frenet's theory in low dimensional manifolds is reached.