Christoffelsymbole

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$\Gamma _{{\color{Red}\mu} {\color{Violet}\nu } }^{{\color{Orange}\alpha}} = \frac{1}{2} {{g}^{{\color{Orange}\alpha}\sigma }}\left( {{g}_{\sigma {\color{Violet}\mu } ,{\color{Red}\nu} }} + {{g}_{\sigma {\color{Red}\nu} ,{\color{Violet}\mu } }} - {{g}_{{\color{Red}\mu} {\color{Violet}\nu } ,\sigma }} \right)$

$\Gamma _{\mu \nu }^{\alpha }=\frac{\color{Brown}\partial {{x}^{\alpha }}}{\partial {{\xi }^{\beta }}}\frac{{{\partial }^{2}}{{\xi }^{\beta }}}{\color{Brown}\partial {{x}^{\mu }}\partial {{x}^{\nu }}}$

Verhalten bei Koordinatentransformation

$\Gamma{'}_{\mu \nu }^{\alpha }=\frac{\partial x{{'}^{\alpha }}}{\partial {{x}^{\beta }}}\frac{\partial {{x}^{\rho }}}{\partial x{{'}^{\mu }}}\frac{\partial {{x}^{\sigma }}}{\partial x{{'}^{\nu }}}\Gamma _{\rho \sigma }^{\beta }+\frac{\color{Brown}\partial x{{'}^{\alpha }}}{\partial {{x}^{\beta }}}\frac{{{\partial }^{2}}{{x}^{\beta }}}{\color{Brown}\partial x{{'}^{\mu }}\partial x{{'}^{\nu }}}$

Christoffelsymbole

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Verhalten bei Koordinatentransformation

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