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embedded submanifold

См. также в других словарях:

  • Submanifold — In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S rarr; M satisfies certain properties. There are different types of submanifolds depending on exactly which …   Wikipedia

  • Clifford torus — In geometric topology, the Clifford torus is a special kind of torus sitting inside R4. Alternatively, it can be seen as a torus sitting inside C2 since C2 is topologically the same space as R4. Furthermore, every point of the Clifford torus lies …   Wikipedia

  • Darboux frame — In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame as applied to surface geometry. A Darboux frame exists at any non umbilic point of a surface …   Wikipedia

  • Integrability conditions for differential systems — In mathematics, certain systems of partial differential equations are usefully formulated, from the point of view of their underlying geometric and algebraic structure, in terms of a system of differential forms. The idea is to take advantage of… …   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

  • Geometric flow — In mathematics, specifically differential geometry, a geometric flow is the gradient flow associated to a functional on a manifold which has a geometric interpretation, usually associated with some extrinsic or intrinsic curvature. They can be… …   Wikipedia

  • Tangent space — In mathematics, the tangent space of a manifold is a concept which facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector pointing from… …   Wikipedia

  • 3-sphere — Stereographic projection of the hypersphere s parallels (red), meridians (blue) and hypermeridians (green). Because this projection is conformal, the curves intersect each other orthogonally (in the yellow points) as in 4D. All curves are circles …   Wikipedia

  • Homotopy — This article is about topology. For chemistry, see Homotopic groups. The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy. In topology, two continuous functions from one… …   Wikipedia

  • JSJ decomposition — In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: Irreducible orientable closed (i.e., compact and without boundary) 3 manifolds have a unique (up to isotopy)… …   Wikipedia

  • CR manifold — In mathematics, a CR manifold is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Formally, a CR manifold is a… …   Wikipedia

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