which is skew-symmetrical in all pairs of indices, by cyclic interchange and addition.
If, in (78), we replace
by the fundamental tensor,
, then the right-hand side vanishes identically; an analogous statement holds for (80) with respect to
; that is, the co-variant derivatives of the fundamental tensor vanish. That this must be so we see directly in the local system of co-ordinates.
In case
