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covariant derivative
(redirected from Covariant differentiation)

   Also found in: Wikipedia 0.02 sec.
covariant derivative [kō′ver·ē·ənt də′riv·əd·iv]
(mathematics)
For a tensor field at a pointPof an affine space, a new tensor field equal to the difference between the derivative of the original field defined in the ordinary manner and the derivative of a field whose value at points close toPare parallel to the value of the original field atPas specified by the affine connection.


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[rho]] being unit orthogonal vector fields, [nabla] denotes the operator of covariant differentiation with respect to the metric tensor g.
He begins with manifolds, tensors and exterior forms and progresses to such topics as the integration of differential forms and the Lie derivative, the Poincare Lemma and potentials, Monkowski space, covariant differentiation and curvature, relativity, Betti numbers and De Rham's theorem, harmonic forms, the Aharonov-Bohm effect, and Yang- Mills fields.
j](t)} dV = 0 (11) Use of the product rule for covariant differentiation and application of the divergence theorem gives: [[integral].
 
 
 
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