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metric with nonnegative curvature

См. также в других словарях:

  • 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

  • Riemannian geometry — Elliptic geometry is also sometimes called Riemannian geometry. Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric , i.e. with an inner product on the tangent… …   Wikipedia

  • Polyhedral space — In mathematics, specifically in metric geometry, a polyhedral space is a certain metric space. A (Euclidean) polyhedral space is a (usually finite) simplicial complex in which every simplex has a flat metric. (Other spaces of interest are… …   Wikipedia

  • Symmetric space — In differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to make this precise. In Riemannian… …   Wikipedia

  • Gauss–Codazzi equations — In Riemannian geometry, the Gauss–Codazzi–Mainardi equations are fundamental equations in the theory of embedded hypersurfaces in a Euclidean space, and more generally submanifolds of Riemannian manifolds. They also have applications for embedded …   Wikipedia

  • solids, mechanics of — ▪ physics Introduction       science concerned with the stressing (stress), deformation (deformation and flow), and failure of solid materials and structures.       What, then, is a solid? Any material, fluid or solid, can support normal forces.… …   Universalium

  • 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

  • Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …   Wikipedia

  • Euclidean space — Every point in three dimensional Euclidean space is determined by three coordinates. In mathematics, Euclidean space is the Euclidean plane and three dimensional space of Euclidean geometry, as well as the generalizations of these notions to… …   Wikipedia

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