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r16
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this is my first post on this site but it looks like the sort of ppl that i would like to associate myself with.
Unfourtanately, I have not had any formal schooling for any mathematics above calculus but i have read a few books and papers and am trying to make due.
I was studying about the cartan's first structure equation and was looking at this proof :
http://www.pzgnet.cc/images/cartan/eq1.png
where [tex] \nabla_x [/tex] is a koszul connection, [tex] e_i [/tex] is a basis and [tex] \partial_j A^j_i [/tex] is a change of basis from e and [tex] \omega [/tex] is a standard connection in the actual equation :
http://www.pzgnet.cc/images/cartan/eq2.png
In step 3 why can the exterior derivitave be applied to [tex] A^j_i [/tex]?
I am no impact no idea on this step and it seems quite important so i don't want to skip it. Any ideas what I am missing?
**nb in equation 2 [tex] \omega^i_j [/tex] should be [tex] \omega^j_i [/tex]
Unfourtanately, I have not had any formal schooling for any mathematics above calculus but i have read a few books and papers and am trying to make due.
I was studying about the cartan's first structure equation and was looking at this proof :
http://www.pzgnet.cc/images/cartan/eq1.png
where [tex] \nabla_x [/tex] is a koszul connection, [tex] e_i [/tex] is a basis and [tex] \partial_j A^j_i [/tex] is a change of basis from e and [tex] \omega [/tex] is a standard connection in the actual equation :
http://www.pzgnet.cc/images/cartan/eq2.png
In step 3 why can the exterior derivitave be applied to [tex] A^j_i [/tex]?
I am no impact no idea on this step and it seems quite important so i don't want to skip it. Any ideas what I am missing?
**nb in equation 2 [tex] \omega^i_j [/tex] should be [tex] \omega^j_i [/tex]
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