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| [[Bild:KovarianteAbleitung.png]]
| | <math>{A^\lambda }_{\mu ;\nu } = \frac{{\partial {A^\lambda }_\mu }}{{\partial {x^\nu }}} + \Gamma _{\rho \nu }^\lambda {A^\rho }_\mu - \Gamma _{\mu \nu }^\rho {A^\lambda }_\rho |
| <source lang="latex"> | |
| \begin{align} | |
| T_{{\color{Orange}rs...}; \color{Red}l}^{\color{Blue}ik...}
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| =
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| T_{{\color{Orange}rs...}, \color{Red}l}^{\color{Blue} ik...}&
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| +
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| \Gamma _{ m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{m\color{Blue}k...}\quad&&
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| +
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| \Gamma _{m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{{\color{Blue}r}m\color{Blue}...}... &\quad&
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| {\color{Blue}\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden oberen Index}} \\
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| & +
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| \Gamma _{\color{Orange}r\color{Red}l}^{m}T_{m\color{Orange}s...}^{ \color{Blue}ik...}\quad&& | |
| +
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| \Gamma _{\color{Orange}r\color{Red}l}^{m}T_{{\color{Orange}r}m\color{Orange}...}^{ \color{Blue}ik...}...&&
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| \color{Orange}{\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden unteren Index}} \\
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| \end{align}
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| </source>
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| | |
| :<math>
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| \begin{align}
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| T_{{\color{Orange}rs...}; \color{Red}l}^{\color{Blue}ik...}
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| =
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| T_{{\color{Orange}rs...}, \color{Red}l}^{\color{Blue} ik...}&
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| + | |
| \Gamma _{ m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{m\color{Blue}k...}\quad&& | |
| +
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| \Gamma _{m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{{\color{Blue}r}m\color{Blue}...}... &\quad&
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| {\color{Blue}\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden oberen Index}} \\
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| & +
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| \Gamma _{\color{Orange}r\color{Red}l}^{m}T_{m\color{Orange}s...}^{ \color{Blue}ik...}\quad&&
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| +
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| \Gamma _{\color{Orange}r\color{Red}l}^{m}T_{{\color{Orange}r}m\color{Orange}...}^{ \color{Blue}ik...}...&&
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| \color{Orange}{\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden unteren Index}} \\
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| \end{align}
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| </math> | | </math> |
|
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|
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| :<math>
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| {A^{\color{Violet}\lambda }}_{{\color{Orange}\mu};{\color{Red}\nu} }
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| =
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| \frac{{\partial {A^{\color{Violet}\lambda }}_{\color{Orange}\mu}}}
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| {{\partial {x^{\color{Red}\nu} }}}
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| +
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| \Gamma _{\rho {\color{Red}\nu} }^{\color{Violet}\lambda }
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| {A^\rho }_{\color{Orange}\mu}
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| -
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| \Gamma _{{\color{Orange}\mu}{\color{Red}\nu} }^\rho
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| {A^{\color{Violet}\lambda }}_\rho
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| </math>
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|
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| == Eigenschaften ==
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| * erhält Tensoreingeschaft <-> Unterschied zur [[gewöhnlichen Ableitung]]
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|
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| [[Kategorie:Tensor]]
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