Just started self teaching myself differential geometry and tried to find the christoffel symbols of the second kind for 2d polar coordinates. I am checking to see if I did everything correctly.(adsbygoogle = window.adsbygoogle || []).push({});

With a line element of:

therefore the metric should be:

The christoffel symbols of the second kind can be found by:

And the non-zero christoffel symbols I found:

I noticed since is symmetric it is non-zero when m=k so summing over k is not needed, i do not know if I missed anything by doing this.

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# Metric of polar coordinates

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