Principles of Tensor Calculus by Taha Sochi

Author:Taha Sochi [Sochi, Taha]
Language: eng
Format: azw3, epub
Publisher: CreateSpace
Published: 2017-08-12T04:00:00+00:00

 = δijlm

(Eq. 199↑)

that is: (205) δijklmk = δijlm

Similar identities can be obtained from contracting two corresponding indices of the nD generalized Kronecker delta to obtain (n − 1)D generalized Kronecker delta, e.g. (206) δijlj = δil

which can be simply verified following the former example, that is: (207)

Returning to the widely used epsilon-delta identity of Eq. 191↑, if we consider Eq. 205↑ plus the above identities which correlate the permutation tensor, the generalized Kronecker delta tensor and the ordinary Kronecker delta tensor, then an identity equivalent to Eq. 191↑ that involves only the generalized and ordinary Kronecker deltas can be obtained, that is (see Footnote 20 in § 8↓): (208) ϵijk ϵlmk = δijklmk

(Eq. 201↑)  = δijlm

(Eq. 205↑)

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