- #1
player1_1_1
- 112
- 0
Hell
let make a metric tensor, let it make simple, for random 2-dimensional 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? don't I have to use covariant derivative? thanks for answer!
let make a metric tensor, let it make simple, for random 2-dimensional 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? don't I have to use covariant derivative? thanks for answer!