i am trying to verify this equality so here is what i did so far:
then since i now have
and i seem to be stuck here. have what i've been doing so far correct and if so how may i continue. thanks.
i am trying to verify this equality so here is what i did so far:
then since i now have
and i seem to be stuck here. have what i've been doing so far correct and if so how may i continue. thanks.
oops i had a few typos in the christoffel symbols. now that they are fixed i had some nice cancellations.
now i am left with:
and since the derivative of g is 0 and since it is a tensor and has a derivative of zero in cartesian coordinates, it must have the same for all coordinates and therefore the identity is 0 = 0. is this the correct reasoning? thanks.