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connection geometry

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  • Connection (algebraic framework) — Geometry of quantum systems (e.g., noncommutative geometry and supergeometry) is mainly phrased in algebraic terms of modules and algebras. Connections on modules are generalization of a linear connection on a smooth vector bundle written as a… …   Wikipedia

  • Geometry — (Greek γεωμετρία ; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. Initially a body of… …   Wikipedia

  • Connection (mathematics) — In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of… …   Wikipedia

  • Connection form — In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan …   Wikipedia

  • Connection (vector bundle) — This article is about connections on vector bundles. See connection (mathematics) for other types of connections in mathematics. In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; …   Wikipedia

  • Connection (principal bundle) — This article is about connections on principal bundles. See connection (mathematics) for other types of connections in mathematics. In mathematics, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way …   Wikipedia

  • Connection — Connect, connection, connections, connected, or connectivity may refer to: Contents 1 Mathematics 2 Technology 3 Media …   Wikipedia

  • geometry — /jee om i tree/, n. 1. the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties… …   Universalium

  • History of geometry — Geometry (Greek γεωμετρία ; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre modern mathematics, the other being the study of numbers. Classic geometry… …   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

  • 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

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