vector bundle chart

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• Vector field — In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a (locally) Euclidean space.Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid… …   Wikipedia

• Tangent bundle — In mathematics, the tangent bundle of a smooth (or differentiable) manifold M , denoted by T ( M ) or just TM , is the disjoint unionThe disjoint union assures that for any two points x 1 and x 2 of manifold M the tangent spaces T 1 and T 2 have… …   Wikipedia

• Fiber bundle — In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which looks locally like a product space. It may have a different global topological structure in that the space as a whole may not be homeomorphic to a… …   Wikipedia

• Glossary of differential geometry and topology — This is a glossary of terms specific to differential geometry and differential topology. The following two glossaries are closely related: *Glossary of general topology *Glossary of Riemannian and metric geometry.See also: *List of differential… …   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

• Frame fields in general relativity — In general relativity, a frame field (also called a tetrad or vierbein) is a set of four orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian manifold that is physically interpreted as a model of spacetime. The… …   Wikipedia

• Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …   Wikipedia

• Cartan connection — In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the …   Wikipedia

• Pushforward (differential) — Suppose that phi; : M → N is a smooth map between smooth manifolds; then the differential of phi; at a point x is, in some sense, the best linear approximation of phi; near x . It can be viewed as generalization of the total derivative of… …   Wikipedia

• Density on a manifold — In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold which can be integrated in an intrinsic manner. Abstractly, a density is a section of a certain trivial line bundle,… …   Wikipedia

• Microbundle — In mathematics, a microbundle is a generalization of the concept of vector bundle, introduced by the American mathematician John Milnor in 1964.[1] It allows the creation of bundle like objects in situations where they would not ordinarily be… …   Wikipedia