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constant curvature space

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  • Constant curvature — See also: Space form In mathematics, constant curvature in differential geometry is a concept most commonly applied to surfaces. For those the scalar curvature is a single number determining the local geometry, and its constancy has the obvious… …   Wikipedia

  • Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …   Wikipedia

  • Space form — In mathematics, a space form is a complete Riemannian manifold M of constant sectional curvature K . Reduction to generalized crystallographyIt is a theorem of Riemannian geometry that the universal cover of an n dimensional space form M^n with… …   Wikipedia

  • Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… …   Wikipedia

  • Space weathering — is a blanket term used for a number of processes that act on any body exposed to the harsh space environment. Airless bodies (including the Moon, Mercury, the asteroids, comets, and some of the moons of other planets) incur many weathering… …   Wikipedia

  • space-time — /spays tuym /, n. 1. Also called space time continuum. the four dimensional continuum, having three spatial coordinates and one temporal coordinate, in which all physical quantities may be located. 2. the physical reality that exists within this… …   Universalium

  • Ricci curvature — In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci Curbastro, provides one way of measuring the degree to which the geometry determined by a given Riemannian metric might differ from that of ordinary Euclidean n… …   Wikipedia

  • Sectional curvature — In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K(σp) depends on a two dimensional plane σp in the tangent space at p. It is the Gaussian curvature of… …   Wikipedia

  • Gaussian curvature — In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ 1 and κ 2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how… …   Wikipedia

  • CAT(k) space — In mathematics, a CAT( k ) space is a specific type of metric space. Intuitively, triangles in a CAT( k ) space are slimmer than corresponding model triangles in a standard space of constant curvature k . In a CAT( k ) space, the curvature is… …   Wikipedia

  • de Sitter space — In mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n dimensional de Sitter space , denoted dSn, is the Lorentzian manifold analog of an n sphere (with its… …   Wikipedia

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