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Affine connection

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Affine connection
In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space. The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity). The terminology is due to Cartan and has its origins in the identification of tangent spaces in Euclidean space Rn by translation: the idea is that a choice of affine connection makes a manifold look infinitesimally like Euclidean space not just smoothly, but as an affine space.

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专业字典

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affine connection
affine coordinates 仿射坐标 平行坐标

Glosarium Pusat Bahasa Depdiknas Indonesia

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affine connection
B: (Matematika) hubungan afin

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Math

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affine connection
التصاق آفين

Mathematics Glossary - Mohammad Reza Majidee

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affine connection
ارتباط مستوي ، همبستگي خويشاوند ، همبندش مستوي ، ارتباط آفين ، هموستار آفين ، هموستار همگر
ساختاري روي يک فضاي n بعدي که به ازاي هر جفت نقطه ي همسايه ي P و Q قاعده اي مشخّص مي کند که بنابر آن، بردار معيّني در Q به هر بردار در P وابسته مي شود؛ اين دو بردار را موازي گويند.



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