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Connection (Mathematics)
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Geliefert zwischen Do., 29.01.2026 und Fr., 30.01.2026
Details
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 data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for transporting tangent vectors to a manifold from one point to another along a curve. An affine connection is typically given in the form of a covariant derivative, which gives a means for taking directional derivatives of vector fields: the infinitesimal transport of a vector field in a given direction. Connections are of central importance in modern geometry in large part because they allow a comparison between the local geometry at one point and the local geometry at another point. Differential geometry embraces several variations on the connection theme, which fall into two major groups: the infinitesimal and the local theory. The local theory concerns itself primarily with notions of parallel transport and holonomy. The infinitesimal theory concerns itself with the differentiation of geometric data.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130629021
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- EAN 9786130629021
- Format Fachbuch
- Titel Connection (Mathematics)
- Herausgeber Alphascript Publishing
- Anzahl Seiten 168
- Genre Mathematik
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