# Christoffel simbol and derivative from him

1. Feb 3, 2010

### player1_1_1

Hell let make a metric tensor, let it make simple, for random 2-dimentional curved space, ex.
$$g_{jk}=\begin{bmatrix}R&0\\ 0&R\sin\phi\end{bmatrix}$$
where R is constant, and $$\phi,\varphi$$ are variables. Now I have symbol $$g_{jk,l}$$, does it mean just partial derivative
$$\frac{\partial g_{jk}}{\partial x_l}$$?
lets choose $$g_{22}$$ element and symbol $$g_{22,\phi}$$. does it mean
$$\frac{\partial g_{22}}{\partial\phi}=R\cos\phi$$?
and the last: in riemann curvature tensor definition is fragment:
$$\frac{\partial\Gamma^a_{bc}}{\partial x^d}$$
is it just partial derivative of Christoffel simbol? dont I have to use covariant derivative? thanks for answer!

2. Feb 4, 2010