255(5): Vector Format of the Cartan Identity with Timelike Indices

This gives Eqs. (3) and (35) of the attached note. Eq. (35) is a new spin connection resonance structure. The three index Levi Civita symbols with timelike indices are defined systematically from the four index Levi Civita symbol by multiplying with the contravariant or covariant unit vectors.The method is illustrated with the Minkowski metric but any metric may be used. Eqs. (3) and (35) are new and original representations of the Cartan identity which exist along with the structures of the field equations given in the ECE engineering model in vector notation for engineers.


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