Christoffelsymbole: Unterschied zwischen den Versionen
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| (2 dazwischenliegende Versionen von 2 Benutzern werden nicht angezeigt) | |||
| Zeile 6: | Zeile 6: | ||
{{g}_{\sigma {\color{Violet}\mu } ,{\color{Red}\nu} }} | {{g}_{\sigma {\color{Violet}\mu } ,{\color{Red}\nu} }} | ||
+ | + | ||
{{g}_{\sigma {\color{Red}\nu} ,{\color{ | {{g}_{\sigma {\color{Red}\nu} ,{\color{Violet}\mu } }} | ||
- | - | ||
{{g}_{{\color{Red}\mu} {\color{Violet}\nu } ,\sigma }} \right) | {{g}_{{\color{Red}\mu} {\color{Violet}\nu } ,\sigma }} \right) | ||
</math> | </math> | ||
<math>\Gamma _{\mu \nu }^{\alpha }=\frac{\color{ | :<math>\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 }}}</math> | ||
| Zeile 17: | Zeile 17: | ||
<math>\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{\partial x{{'}^{\alpha }}}{\partial {{x}^{\beta }}}\frac{{{\partial }^{2}}{{x}^{\beta }}}{\partial x{{'}^{\mu }}\partial x{{'}^{\nu }}}</math> | :<math>\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 }}}</math> | ||
[[Kategorie:ART]] | |||