covariant derivative

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covariant derivative

[kō′ver·ē·ənt də′riv·əd·iv]
(mathematics)
For a tensor field at a point P of 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 to P are parallel to the value of the original field at P as specified by the affine connection.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Fix now the covariant differential operator [nabla] for [pi].
Let (M,g) be a Riemannian [C.sup.[infinity]]-manifold and [nabla] be the covariant differential operator with respect to the metric tensor g.