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Unformatted text preview: = 1gijl > 0 We see that the proper generalizations of the Kronecker delta are the Euclidean metric tensors, and those of the permutation symbol are f i j k and eijk, which are called permutation tensors or alternators. As defined by Eqs. (6) and (7), the components of Eijk and eijk do not have values 1, -1, or 0 in general coordinates, they are (a, -a, 0) and (l/fi, -l/fi, 0) respectively. Note that the mixed tensor gj is identical with 6; and is constant in all coordinate systems. Fkom Eqs. (3) and (4) we see that (9) gimgmj = 6: . Hence, the determinant .. IgimgmjI = 1gij1 ' 1ga31 = 16;1 = 1....
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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