High Quality Content by WIKIPEDIA articles! In mathematics, the Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Elie Cartan and Hermann Weyl in the early part of the twentieth century: parallel transport, covariant derivative and connection form . These concepts were put in their final form using the language of principal bundles only in the 1950s. The classical nineteenth century approach to the differential geometry of surfaces, due in large part to Carl Friedrich Gauss, has been reworked in this modern framework, which provides the natural setting for the classical theory of the moving frame as well as the Riemannian geometry of higher dimensional Riemannian manifolds. This account is intended as an introduction to the theory of connections. Данное издание представляет собой компиляцию сведений, находящихся в свободном доступе в среде Интернет в целом, и в информационном сетевом ресурсе...

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