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connection (Definition)
CovariantDerivative

"connection" is owned by rspuzio. [ full author list (5) | owner history (1) ]
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See Also: Christoffel symbols, curvature of a circle, sphere theorem from global differential geometry, geodesic, Riemann curvature tensor

Also defines:  covariant derivative, torsion, curvature, torsionless, flat, Christoffel symbol

Attachments:
affine connection (Definition) by rspuzio
Riemann curvature tensor (Definition) by juanman
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Cross-references: bibliography for differential geometry, percentage, affine connection, Elie Cartan, integrate, local coordinates, locally Euclidean, vanishes, anti-symmetric, derivation, tensorial, Lie bracket, bilinear mapping, language, compatible, generate, focus, restriction, frame, defining properties, capacity, type, argument, complete, fibre bundles, cocycle condition, consistent, transition function, local trivializations, diffeomorphism, open set, local trivialization, clear, reference, useful, cotangent, indexed by, associate, object, dimension, representation, action, Lie algebra, column vector, exterior derivative, connection coefficients, matrices, contained, information, coordinate system, surfaces, index, represent, maps, origin, property, equation, transformation, imply, change of coordinates, expression, differential form, infinitesimal, tangent space, collection, relation, tensor, component, operator, partial derivative, mean, imaginary unit, even, plus sign, force, formula, element, field, indices, scalar, scalar multiple, sum, subset, neighborhood, coordinates, directional derivative, cover, product, multiplication, pointwise, group, smooth maps, sections, isomorphic, fibers, Lie group, structure group, vector space, real, ring, smooth, Formalisms, terms, propositions, translate, order, equivalent, tangent bundle, vector bundle, topology, theory, Hilbert space, necessary, accessible, infinite-dimensional, finite-dimensional, differentiation, base point, function, derivative, manifold, vector field, endpoints, difference, sequence, curve, analogy, differential geometry, right, Transform, linear transformations, point, operations, basepoint, analysis, vector, definitions, parallel
There are 106 references to this entry.

This is version 40 of connection, born on 2002-04-28, modified 2007-05-19.
Object id is 2880, canonical name is Connection.
Accessed 39795 times total.

Classification:
AMS MSC53B05 (Differential geometry :: Local differential geometry :: Linear and affine connections)

Pending Errata and Addenda
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coonections. by bahramH on 2005-07-11 05:17:10
Great text on connections : short, concise and extremely readable.

I think these references (as you've noted) by Elie Cartan could be mentionned :

1- "Leçon sur la géométrie des espaces de Rieman", E.Cartan. Gauthier-Villars, Paris, 1963.
This is lecture given by Cartan in 1925.

2- "Sur les variétés à connexion affine et la théorie de la relativité généralisée", E. Cartan, Annales scientifiques de l'ENS, 3ème série, tome 40 (1923), 325-412.
This article (and the following two) are available on line on "Numdam": www.numdam.org
or directly at
 http://www.numdam.org/item?id=ASENS_1923_3_40__325_0
This is an extremely beautifull article.

Regards,
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