tensor notation

Hi all,



Could someone explain, please, how the following expression can be written in component notation according to summation convention?



a^{kj};k + G^j_{km} a^{km} + G^k_{km} a^{mj}



it is the case of general tensors (non Cartesian)

indices k, j, m take values 1, 2, 3

G^j_{km} is Christoffel symbol of the second kind

; denotes partial differentiation (it is not covariant differentiation)



The first term is written a^{1j};1 + a^{2j};2 + a^{3j};3  

the second is G^j_{11} a^{11} + G^j_{12} a^{12} + G^j_{13} a^{13} + G^j_{21} a^{21} + G^j_{22} a^{22} + G^j_{23} a^{23} + G^j_{31} a^{31} + G^j_{32} a^{32}  + G^j_{33} a^{33}

What about the last term? Is k also the summation index, and so \Sum_k \Sum_m G^k_{km} a^{mj} ?







Best regards,

Rudi