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Display information for equation id:math.391.0 on revision:391

* Page found: Riemannscher Krümmungstensor (eq math.391.0)

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Hash: dc6e8906e306d2ec0cd46d8462866ddd

TeX (original user input):

{R^{\color{Violet}\alpha}} _
{{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}
 =
{\partial _{\color{Orange}\mu}}
\Gamma _{{\color{WildStrawberry}\beta} {\color{Red}\nu} }^{\color{Violet}\alpha}
 -
{\partial _{{\color{Orange}\mu} {\color{Red}\nu}}}
\Gamma _{{\color{WildStrawberry}\beta} {\color{Orange}\mu} }^{\color{Violet}\alpha}
 +
 \Gamma _{\sigma {\color{Orange}\mu} } ^ {\color{Violet}\alpha}
 \Gamma _{{\color{WildStrawberry}\beta} {\color{Red}\nu} }^\sigma
 -
 \Gamma _{\sigma {\color{Red}\nu}} ^ {\color{Violet}\alpha}
 \Gamma _{{\color{WildStrawberry}\beta} {\color{Orange}\mu} }^\sigma

TeX (checked):

{R^{\color {Violet}\alpha }}_{{\color {WildStrawberry}\beta }{\color {Orange}\mu }{\color {Red}\nu }}={\partial _{\color {Orange}\mu }}\Gamma _{{\color {WildStrawberry}\beta }{\color {Red}\nu }}^{\color {Violet}\alpha }-{\partial _{{\color {Orange}\mu }{\color {Red}\nu }}}\Gamma _{{\color {WildStrawberry}\beta }{\color {Orange}\mu }}^{\color {Violet}\alpha }+\Gamma _{\sigma {\color {Orange}\mu }}^{\color {Violet}\alpha }\Gamma _{{\color {WildStrawberry}\beta }{\color {Red}\nu }}^{\sigma }-\Gamma _{\sigma {\color {Red}\nu }}^{\color {Violet}\alpha }\Gamma _{{\color {WildStrawberry}\beta }{\color {Orange}\mu }}^{\sigma }

LaTeXML (experimentell; verwendet MathML) rendering

MathML (0 B / 8 B) :

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MathML (3.213 KB / 371 B) :

{R^{α}}_{β μ ν} = \partial_{μ} Γ_{β ν}^{α} - \partial_{μ ν} Γ_{β μ}^{α} + Γ_{σ μ}^{α} Γ_{β ν}^{σ} - Γ_{σ ν}^{α} Γ_{β μ}^{σ}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>α</mi></mstyle></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>β</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>μ</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>ν</mi></mstyle></mrow></mrow></mrow></msub><mo stretchy="false">=</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>μ</mi></mstyle></mrow></mrow></msub><msubsup><mi>Γ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>β</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>ν</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>α</mi></mstyle></mrow></mrow></msubsup><mo stretchy="false">−</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>μ</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>ν</mi></mstyle></mrow></mrow></mrow></msub><msubsup><mi>Γ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>β</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>μ</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>α</mi></mstyle></mrow></mrow></msubsup><mo stretchy="false">+</mo><msubsup><mi>Γ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>σ</mi><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>μ</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>α</mi></mstyle></mrow></mrow></msubsup><msubsup><mi>Γ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>β</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>ν</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow></msubsup><mo stretchy="false">−</mo><msubsup><mi>Γ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>σ</mi><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>ν</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>α</mi></mstyle></mrow></mrow></msubsup><msubsup><mi>Γ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>β</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>μ</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>σ</mi></mrow></msubsup></mstyle></mrow></math>

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Identifiers

$R$

$α$

$β$

$μ$

$ν$

$μ$

$Γ$

$β$

$ν$

$α$

$μ$

$ν$

$Γ$

$β$

$μ$

$α$

$Γ$

$σ$

$μ$

$α$

$Γ$

$β$

$ν$

$σ$

$Γ$

$σ$

$ν$

$α$

$Γ$

$β$

$μ$

$σ$

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