2022-02-06   03519

Covariant Derivatives and Curvature

Partial derivatives of tensor fields are generally not tensor fields. The concept of a covariant derivative is a modification of the concept of a partial derivative, defined so that covariant derivatives of tensor fields are still tensor fields. Curvature tensors are defined in terms of covariant derivatives. General relativity is formulated with the help of a special covariant derivative that is metric-compatible and torsion-free.

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www.cphysics.org updated 2022-09-25