Christoffelsymbole: Unterschied zwischen den Versionen
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Die Seite wurde neu angelegt: <math>\Gamma _{\nu \rho }^\mu = \frac{1}{2}{g^{\mu \alpha }}\left( {{\partial _\rho }{g_{\alpha \nu }} + {\partial _\nu }{g_{\alpha \rho }} - {\partial _\alpha }{g_{\n... |
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<math>\Gamma _{\nu \ | <math> | ||
\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) | |||
</math> | |||
:<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> | |||
== Verhalten bei Koordinatentransformation == | |||
:<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]] | |||