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Display information for equation id:math.1802.38 on revision:1802

* Page found: Kovariante Schreibweise der Relativitätstheorie (eq math.1802.38)

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Kovariante Schreibweise der Relativitätstheorie Eq: math.1802.38

Hash: c7ae09ae90baa820aa55532aa6a58e02

TeX (original user input):

\begin{align}

& {{g}^{ik}}:={{\delta }^{ik}}={{\delta }^{i}}_{k}\quad f\ddot{u}r\ k=0 \\

& {{g}^{ik}}:={{\delta }^{ik}}=-{{\delta }^{i}}_{k}\quad f\ddot{u}r\ k=1,2,3 \\

& {{g}^{ik}}:={{\delta }^{ik}}=\left( \begin{matrix}

1 & {} & {} & {}  \\

{} & -1 & {} & {}  \\

{} & {} & -1 & {}  \\

{} & {} & {} & -1  \\

\end{matrix} \right)={{g}_{ik}} \\

& {{g}^{ik}}{{a}_{k}}={{\delta }^{ik}}{{a}_{k}}={{a}_{i}}\quad f\ddot{u}r\ i=0\Rightarrow {{a}_{i}}={{a}^{i}} \\

& {{g}^{ik}}{{a}_{k}}={{\delta }^{ik}}{{a}_{k}}=-{{a}_{i}}\quad f\ddot{u}r\ i=1,2,3\Rightarrow -{{a}_{i}}={{a}^{i}} \\

\end{align}

TeX (checked):

{\begin{aligned}&{{g}^{ik}}:={{\delta }^{ik}}={{\delta }^{i}}_{k}\quad f{\ddot {u}}r\ k=0\\&{{g}^{ik}}:={{\delta }^{ik}}=-{{\delta }^{i}}_{k}\quad f{\ddot {u}}r\ k=1,2,3\\&{{g}^{ik}}:={{\delta }^{ik}}=\left({\begin{matrix}1&{}&{}&{}\\{}&-1&{}&{}\\{}&{}&-1&{}\\{}&{}&{}&-1\\\end{matrix}}\right)={{g}_{ik}}\\&{{g}^{ik}}{{a}_{k}}={{\delta }^{ik}}{{a}_{k}}={{a}_{i}}\quad f{\ddot {u}}r\ i=0\Rightarrow {{a}_{i}}={{a}^{i}}\\&{{g}^{ik}}{{a}_{k}}={{\delta }^{ik}}{{a}_{k}}=-{{a}_{i}}\quad f{\ddot {u}}r\ i=1,2,3\Rightarrow -{{a}_{i}}={{a}^{i}}\\\end{aligned}}

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\begin{aligned} g^{i k} : = δ^{i k} = {δ^{i}}_{k} f \ddot{u} r k = 0 \\ g^{i k} : = δ^{i k} = - {δ^{i}}_{k} f \ddot{u} r k = 1, 2, 3 \\ g^{i k} : = δ^{i k} = (\begin{matrix} 1 \\ - 1 \\ - 1 \\ - 1 \end{matrix}) = g_{i k} \\ g^{i k} a_{k} = δ^{i k} a_{k} = a_{i} f \ddot{u} r i = 0 \Rightarrow a_{i} = a^{i} \\ g^{i k} a_{k} = δ^{i k} a_{k} = - a_{i} f \ddot{u} r i = 1, 2, 3 \Rightarrow - a_{i} = a^{i} \end{aligned}

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Identifiers

$g$

$i$

$k$

$δ$

$i$

$k$

$δ$

$i$

$k$

$f$

$\ddot{u}$

$r$

$k$

$g$

$i$

$k$

$δ$

$i$

$k$

$δ$

$i$

$k$

$f$

$\ddot{u}$

$r$

$k$

$g$

$i$

$k$

$δ$

$i$

$k$

$g_{i k}$

$g$

$i$

$k$

$a_{k}$

$δ$

$i$

$k$

$a_{k}$

$a_{i}$

$f$

$\ddot{u}$

$r$

$i$

$a_{i}$

$a$

$i$

$g$

$i$

$k$

$a_{k}$

$δ$

$i$

$k$

$a_{k}$

$a_{i}$

$f$

$\ddot{u}$

$r$

$i$

$a_{i}$

$a$

$i$

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