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