covariant derivative in a sentence

In the special case of inertial frames, the Fermi Walker derivatives reduce to covariant derivatives.
Note that the partial derivatives may be written in terms of covariant derivatives and Christoffel symbols as
where \ nabla _ \ mu is the general-relativistic covariant derivative of a spinor.
We introduce an arbitrary covariant derivative via
The gauge covariant derivative transforms similarly.

that is we trace the covariant derivative on the " first two " covariant indices.
Ricci calculus is the modern formalism and notation for tensor indices : indicating partial and covariant derivatives.
Of particular note is their concept of a "'dynamical covariant derivative " '.
The symbol \ partial _ k denotes partial derivative, while \ nabla _ k denotes covariant derivative.
The covariant derivative \ nabla _ a is defined to annihilate the tetrad E _ a ^ I.

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