Notion of Parallelism on a Generic Manifold and Consequent Geometrical Specification of the Riemannian Curvature

With regard to classical differential geometry, this paper written in 1916 by T. Levi-Civita introduces the notion of parallelism for a Riemannian manifold of arbitrary dimensions. It also provides a geometrical explanation for the Riemannian curvature and at the same time significantly reduces the mathematical formalism compared with the scientific literature of the time.