basis of manifold

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• Manifold (magazine) — Manifold was a mathematical magazine published at the University of Warwick. Its philosophy was It is possible to be serious about mathematics, without being solemn. Its best known editor was the mathematician Ian Stewart who edited the magazine… …   Wikipedia

• Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   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

• Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… …   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

• Leek and Manifold Valley Light Railway — Infobox rail railroad name=Leek and Manifold Valley Light Railway gauge=RailGauge|30 start year=1904 end year=1934 length=8 frac14; miles hq city=Leek locale=England successor=AbandonedThe Leek and Manifold Valley Light Railway (L MVLR) was a… …   Wikipedia

• Parallelizable manifold — In mathematics, a parallelizable manifold M is a smooth manifold of dimension n having vector fields: V 1, ..., V n , such that at any point P of M the tangent vectors: V i , P provide a basis of the tangent space at P . Equivalently, the tangent …   Wikipedia

• Topological manifold — In mathematics, a topological manifold is a Hausdorff topological space which looks locally like Euclidean space in a sense defined below. Topological manifolds form an important class of topological spaces with applications throughout… …   Wikipedia

• Orthonormal basis — In mathematics, particularly linear algebra, an orthonormal basis for inner product space V with finite dimension is a basis for V whose vectors are orthonormal.[1][2][3] For example, the standard basis for a Euclidean space Rn is an orthonormal… …   Wikipedia

• Coordinate-induced basis — In mathematics, a coordinate induced basis is a basis for the tangent space or cotangent space of a manifold that is induced by a certain coordinate system. Given the coordinate system xa, the coordinate induced basis ea of the tangent space is… …   Wikipedia

• Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …   Wikipedia