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geodesic parallel

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  • Parallel (geometry) — Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid s… …   Wikipedia

  • Parallel transport — In geometry, parallel transport is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection… …   Wikipedia

  • Geodesic — [ great circle arcs.] In mathematics, a geodesic IPA|/ˌdʒiəˈdɛsɪk, ˈdisɪk/ [jee uh des ik, dee sik] is a generalization of the notion of a straight line to curved spaces . In presence of a metric, geodesics are defined to be (locally) the… …   Wikipedia

  • Geodesic (general relativity) — This article is about the use of geodesics in general relativity. For the general concept in geometry, see geodesic. General relativity Introduction Mathematical formulation Resources …   Wikipedia

  • Geodesic deviation equation — In differential geometry, the geodesic deviation equation is an equation involving the Riemann curvature tensor, which measures the change in separation of neighbouring geodesics. In the language of mechanics it measures the rate of relative… …   Wikipedia

  • geodesic dome — a light, domelike structure developed by R. Buckminster Fuller to combine the properties of the tetrahedron and the sphere and consisting essentially of a grid of compression or tension members lying upon or parallel to great circles running in… …   Universalium

  • Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Mathematics of general relativity — For a generally accessible and less technical introduction to the topic, see Introduction to mathematics of general relativity. General relativity Introduction Mathematical formulation Resources …   Wikipedia

  • Penrose-Hawking singularity theorems — The Penrose Hawking singularity theorems are a set of results in general relativity which attempt to answer the question of whether gravity is necessarily singular. These theorems answer this question affirmatively for matter satisfying… …   Wikipedia

  • Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …   Wikipedia

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