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According to my script, a connection [tex]\nabla_v[/tex] is symmetric if the following holds (I assume for every pair of vectors):

[tex]\nabla_v w - \nabla_w v =[v,w][/tex]

What is the idea behind that? Why are we interested in that kind of symmetry (not for instance 0 instead of the commutator)?

Thanks for any advice!

Angelos

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# Definition of a symmetric connection

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