covariant derivative

(redirected from Covariant differential)

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.
References in periodicals archive ?
infinity]]-manifold and [nabla] be the covariant differential operator with respect to the metric tensor g.
BC) if its covariant differential [nabla]X has no zero components only in two directions.