geodesic completeness

geodesic completeness
мат. геодезическая полнота

Большой англо-русский и русско-английский словарь. 2001.

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  • Geodesic manifold — In mathematics, a geodesic manifold (or geodesically complete manifold) is a surface on which any two points can be joined by a shortest path, called a geodesic.DefinitionLet (M, g) be a (connected) (pseudo ) Riemannian manifold, and let gamma :… …   Wikipedia

  • Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… …   Wikipedia

  • Hopf–Rinow theorem — In mathematics, the Hopf–Rinow theorem is a set of statements about the geodesic completeness of Riemannian manifolds. It is named after Heinz Hopf and his student Willi Rinow (1907–1979). Statement of the theorem Let (M, g) be a connected… …   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

  • Geodesics as Hamiltonian flows — In mathematics, the geodesic equations are second order non linear differential equations, and are commonly presented in the form of Euler–Lagrange equations of motion. However, they can also be presented as a set of coupled first order equations …   Wikipedia

  • Hamiltonian mechanics — is a re formulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton. It arose from Lagrangian mechanics, a previous re formulation of classical mechanics introduced by Joseph Louis Lagrange in 1788 …   Wikipedia

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  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Shape of the Universe — Edge of the Universe redirects here. For the Bee Gees song, see Edge of the Universe (song). The local geometry of the universe is determined by whether Omega is less than, equal to or greater than 1. From top to bottom: a spherical universe, a… …   Wikipedia

  • Calculus of variations — is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite …   Wikipedia

  • List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia


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