In previous talks, SRVF method has been discussed as a powerful and efficient way to analyze collections of curves in a Euclidean space. However, in many applications the data to be analyzed consists of trajectories in a manifold, rather than in a Euclidean space. Examples include hurricane paths on the surface of the earth, paths of covariance matrices that arise in the study of brain connectivity, and paths of images that lie in a shape space. The comparison of curves in a manifold is more subtle than in a Euclidean space, because one cannot subtract velocity vectors that lie in two different tangent spaces! In this talk, we discuss several methods of adapting the SRVF method to this situation, and comment on the advantages and disadvantages of each method.