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Display information for equation id:math.403.0 on revision:403

* Page found: Riemannscher Krümmungstensor (eq math.403.0)

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Riemannscher Krümmungstensor Eq: math.404.0

Hash: 0674dcde0946de535194e26dd6531d80

TeX (original user input):

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

TeX (checked):

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

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MathML (3.175 KB / 347 B) :

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

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><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>&#x03B1;</mi></mstyle></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>&#x03B2;</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>&#x03BC;</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>&#x03BD;</mi></mstyle></mrow></mrow></mrow></msub><mo>=</mo><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>&#x03B2;</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>&#x03BC;</mi></mstyle></mrow><mo>,</mo><mstyle mathcolor="#ED1B23"><mi>&#x03BD;</mi></mstyle></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>&#x03B1;</mi></mstyle></mrow></mrow></msubsup><mo>&#x2212;</mo><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>&#x03B2;</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>&#x03BD;</mi></mstyle></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>&#x03BC;</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>&#x03B1;</mi></mstyle></mrow></mrow></msubsup><mo>+</mo><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>&#x03B2;</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>&#x03BC;</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msubsup><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>&#x03BD;</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>&#x03B1;</mi></mstyle></mrow></mrow></msubsup><mo>&#x2212;</mo><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#EE2967"><mi>&#x03B2;</mi></mstyle></mrow><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#ED1B23"><mi>&#x03BD;</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi></mrow></msubsup><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>&#x03BC;</mi></mstyle></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>&#x03B1;</mi></mstyle></mrow></mrow></msubsup></mstyle></mrow></math>

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Identifiers

$R$

$α$

$β$

$μ$

$ν$

$Γ$

$β$

$μ$

$ν$

$α$

$Γ$

$β$

$ν$

$μ$

$α$

$Γ$

$β$

$μ$

$σ$

$Γ$

$σ$

$ν$

$α$

$Γ$

$β$

$ν$

$σ$

$Γ$

$σ$

$μ$

$α$

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