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Unformatted text preview: (4), we differentiate the equation gij = gi. gj to obtain On permuting the indices i, j, k, we can obtain the derivatives agijlaej, ag,k/aOi. Furthermore, since gi = dR/dei, we have Hence, by substitution, it is easy to show that On multiplying the two sides of the equation by gak and summing over k, the left-hand side becomes I?$, according to the definition on Christoffel symbols. We then multiply the scalar quantity on both sides of the equation by the vectors g, and sum over a to obtain...
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This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.
- Fall '05