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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

2 votes

Riemann's formula for the metric in a normal neighborhood

There is the following way of doing it. Let $\Gamma_{ijk}\equiv g_{is}\Gamma^{s}_{jk}$. Then (see here) $$ g_{jk}(x)=\delta_{jk}+\int_0^1 \alpha ~x^i\Gamma_{[ji]k}(\alpha x)~d\alpha $$ If we expand $\ …
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