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Forums
Mathematics
Differential Geometry
Christoffel symbol and Einstein summation convention
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[QUOTE="Orodruin, post: 6039651, member: 510075"] While what you wrote would be valid, it would not uniquely identify the Christoffel symbols (it completely ignores the symbols ##\Gamma^i_{jk}## for which ##i \neq j## and sums over those where ##j = i##. Your equation has one free index and therefore represents n equations in an n-dimensional space. However, there are ##n^3## connection coefficients (##n^2(n+1)/2## if you require your connection to be torsion free). No it is not, it is a coordinate. [/QUOTE]
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Forums
Mathematics
Differential Geometry
Christoffel symbol and Einstein summation convention
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