11. The connection associated with this covariant derivative is completely determined by the tetrad. 12. The covariant derivative is convenient however because it commutes with raising and lowering indices. 13. Where the semicolon represents a covariant derivative , and the brackets denote anti-symmetrization. 14. The main strategy of the algorithm is to take covariant derivatives of the Riemann tensor. 15. The function is determined by the requirement that the covariant derivative of along is 0. 16. The equation for the covariant derivative can be written down in terms of Christoffel symbols. 17. In general relativity, the partial derivatives used in special relativity are replaced by covariant derivatives . 18. The curvature formula can also be expressed in terms of the second covariant derivative defined as: 19. Sometimes \ Box is used to represent the four-dimensional Levi-Civita covariant derivative . 20. The covariant derivative of a tensor field is presented as an extension of the same concept.
