In mathematics, the Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Élie 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.
Read more about Riemannian Connection On A Surface: Historical Overview, Covariant Derivative, Parallel Transport, Orthonormal Frame Bundle, Principal Connection, Cartan Structural Equations, Holonomy and Curvature, Example: The 2-sphere, Embedded Surfaces, Gauss-Codazzi Equations, Reading Guide, See Also
Famous quotes containing the words connection and/or surface:
“Parents have railed against shelters near schools, but no one has made any connection between the crazed consumerism of our kids and their elders’ cold unconcern toward others. Maybe the homeless are not the only ones who need to spend time in these places to thaw out.”
—Anna Quindlen (b. 1952)
“All beauties contain, like all possible phenomena, something eternal and something transitory,—something absolute and something particular. Absolute and eternal beauty does not exist, or rather it is only an abstraction skimmed from the common surface of different sorts of beauty. The particular element of each beauty comes from the emotions, and as we each have our own particular emotions, so we have our beauty.”
—Charles Baudelaire (1821–1867)