Hell let make a metric tensor, let it make simple, for random 2-dimentional curved space, ex.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]g_{jk}=\begin{bmatrix}R&0\\ 0&R\sin\phi\end{bmatrix}[/tex]

where R is constant, and [tex]\phi,\varphi[/tex] are variables. Now I have symbol [tex]g_{jk,l}[/tex], does it mean just partial derivative

[tex]\frac{\partial g_{jk}}{\partial x_l}[/tex]?

lets choose [tex]g_{22}[/tex] element and symbol [tex]g_{22,\phi}[/tex]. does it mean

[tex]\frac{\partial g_{22}}{\partial\phi}=R\cos\phi[/tex]?

and the last: in riemann curvature tensor definition is fragment:

[tex]\frac{\partial\Gamma^a_{bc}}{\partial x^d}[/tex]

is it just partial derivative of Christoffel simbol? dont I have to use covariant derivative? thanks for answer!

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# Christoffel simbol and derivative from him

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