Christoffelsymbole: Unterschied zwischen den Versionen
Zur Navigation springen
Zur Suche springen
Keine Bearbeitungszusammenfassung |
Keine Bearbeitungszusammenfassung |
||
| 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{Brown}\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{Violet}\partial {{x}^{\alpha }}}{\partial {{\xi }^{\beta }}}\frac{{{\partial }^{2}}{{\xi }^{\beta }}}{\partial {{x}^{\mu }}\partial {{x}^{\nu }}}</math> | |||
== Verhalten bei Koordinatentransformation == | == 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{\partial x{{'}^{\alpha }}}{\partial {{x}^{\beta }}}\frac{{{\partial }^{2}}{{x}^{\beta }}}{\partial x{{'}^{\mu }}\partial x{{'}^{\nu }}}</math> | |||