The article deals with local symmetries of the infinite-order jet space C?-smooth curves in ?m+1 (m ? 1). Transformations under consideration are most general possible: they need not preserve distinction between dependent and independent variables order derivatives may be arbitrarily changed. Unlike common prolonged point Lie's contact transformations, destroy finite-order spaces.

This paper presents a new approach for dimension reduction of data observed on spherical surfaces. Several techniques have been developed in recent years non-euclidean analysis. As pioneer work, (Hauberg 2016) attempted to implement principal curves Riemannian manifolds. However, this uses approximations process manifolds, resulting distorted results. study proposes project onto continuous curv...