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manifold with nonnegative curvature

См. также в других словарях:

  • Inverse mean curvature flow — In the field of differential geometry in mathematics, inverse mean curvature flow (IMCF) is an example of a geometric flow of hypersurfaces a Riemannian manifold (for example, smooth surfaces in 3 dimensional Euclidean space). Intuitively, a… …   Wikipedia

  • 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

  • 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

  • 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

  • Riemannian Penrose inequality — In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem. The… …   Wikipedia

  • Soul theorem — In mathematics, the soul theorem is the following theorem of Riemannian geometry: :If ( M , g ) is a complete non compact Riemannian manifold with sectional curvature K ge; 0, then ( M , g ) has a compact totally convex, totally geodesic… …   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

  • Splitting theorem — The splitting theorem is a classical theorem in Riemannian geometry. It states that if a complete Riemannian manifold M with Ricci curvature :{ m Ric} (M) ge 0 has a straight line, i.e., a geodesic gamma; such that :d(gamma(u),gamma(v))=|u v| for …   Wikipedia

  • Subharmonic function — In mathematics, subharmonic and superharmonic functions are important classes of functions used extensively in partial differential equations, complex analysis and potential theory. Intuitively, subharmonic functions are related to convex… …   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

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