– PhysikWiki

General

Display information for equation id:math.401.3 on revision:401

* Page found: Riemannscher Krümmungstensor (eq math.401.3)

Occurrences on the following pages:

Riemannscher Krümmungstensor Eq: math.404.3

Hash: 14b2de9c73a3133c69ad3dae5ec399f5

TeX (original user input):

R_{{\color{Violet}\alpha}{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}
=
-R_{{\color{WildStrawberry}\beta}{\color{Violet}\alpha} {\color{Orange}\mu} {\color{Red}\nu}}
=
-R_{{\color{Violet}\alpha}{\color{WildStrawberry}\beta}  {\color{Red}\nu}{\color{Orange}\mu}}

TeX (checked):

R_{{\color {Violet}\alpha }{\color {WildStrawberry}\beta }{\color {Orange}\mu }{\color {Red}\nu }}=-R_{{\color {WildStrawberry}\beta }{\color {Violet}\alpha }{\color {Orange}\mu }{\color {Red}\nu }}=-R_{{\color {Violet}\alpha }{\color {WildStrawberry}\beta }{\color {Red}\nu }{\color {Orange}\mu }}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (6.785 KB / 1.057 KB) :

{\displaystyle{\displaystyle R_{{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}% \beta}{\color[rgb]{0,0,0}\mu}{\color[rgb]{0,0,0}\nu}}=-R_{{\color[rgb]{0,0,0}% \beta}{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}\mu}{\color[rgb]{0,0,0}\nu}% }=-R_{{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}\beta}{\color[rgb]{0,0,0}% \nu}{\color[rgb]{0,0,0}\mu}}}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle R_{{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}%&#10;\beta}{\color[rgb]{0,0,0}\mu}{\color[rgb]{0,0,0}\nu}}=-R_{{\color[rgb]{0,0,0}%&#10;\beta}{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}\mu}{\color[rgb]{0,0,0}\nu}%&#10;}=-R_{{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}\beta}{\color[rgb]{0,0,0}%&#10;\nu}{\color[rgb]{0,0,0}\mu}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
      <msub id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">R</mi>
        <mrow id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">
          <mi mathcolor="#000000" id="p1.1.m1.1.2.1.1" xref="p1.1.m1.1.2.1.1.cmml">α</mi>
          <mo id="p1.1.m1.1.2.1.5" xref="p1.1.m1.1.2.1.5.cmml">⁢</mo>
          <mi mathcolor="#000000" id="p1.1.m1.1.2.1.2" xref="p1.1.m1.1.2.1.2.cmml">β</mi>
          <mo id="p1.1.m1.1.2.1.5a" xref="p1.1.m1.1.2.1.5.cmml">⁢</mo>
          <mi mathcolor="#000000" id="p1.1.m1.1.2.1.3" xref="p1.1.m1.1.2.1.3.cmml">μ</mi>
          <mo id="p1.1.m1.1.2.1.5b" xref="p1.1.m1.1.2.1.5.cmml">⁢</mo>
          <mi mathcolor="#000000" id="p1.1.m1.1.2.1.4" xref="p1.1.m1.1.2.1.4.cmml">ν</mi>
        </mrow>
      </msub>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
      <mrow id="p1.1.m1.1.11.3" xref="p1.1.m1.1.11.3.cmml">
        <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">-</mo>
        <msub id="p1.1.m1.1.11.3.1" xref="p1.1.m1.1.11.3.1.cmml">
          <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">R</mi>
          <mrow id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">
            <mi mathcolor="#000000" id="p1.1.m1.1.6.1.1" xref="p1.1.m1.1.6.1.1.cmml">β</mi>
            <mo id="p1.1.m1.1.6.1.5" xref="p1.1.m1.1.6.1.5.cmml">⁢</mo>
            <mi mathcolor="#000000" id="p1.1.m1.1.6.1.2" xref="p1.1.m1.1.6.1.2.cmml">α</mi>
            <mo id="p1.1.m1.1.6.1.5a" xref="p1.1.m1.1.6.1.5.cmml">⁢</mo>
            <mi mathcolor="#000000" id="p1.1.m1.1.6.1.3" xref="p1.1.m1.1.6.1.3.cmml">μ</mi>
            <mo id="p1.1.m1.1.6.1.5b" xref="p1.1.m1.1.6.1.5.cmml">⁢</mo>
            <mi mathcolor="#000000" id="p1.1.m1.1.6.1.4" xref="p1.1.m1.1.6.1.4.cmml">ν</mi>
          </mrow>
        </msub>
      </mrow>
      <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
      <mrow id="p1.1.m1.1.11.4" xref="p1.1.m1.1.11.4.cmml">
        <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">-</mo>
        <msub id="p1.1.m1.1.11.4.1" xref="p1.1.m1.1.11.4.1.cmml">
          <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">R</mi>
          <mrow id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">
            <mi mathcolor="#000000" id="p1.1.m1.1.10.1.1" xref="p1.1.m1.1.10.1.1.cmml">α</mi>
            <mo id="p1.1.m1.1.10.1.5" xref="p1.1.m1.1.10.1.5.cmml">⁢</mo>
            <mi mathcolor="#000000" id="p1.1.m1.1.10.1.2" xref="p1.1.m1.1.10.1.2.cmml">β</mi>
            <mo id="p1.1.m1.1.10.1.5a" xref="p1.1.m1.1.10.1.5.cmml">⁢</mo>
            <mi mathcolor="#000000" id="p1.1.m1.1.10.1.3" xref="p1.1.m1.1.10.1.3.cmml">ν</mi>
            <mo id="p1.1.m1.1.10.1.5b" xref="p1.1.m1.1.10.1.5.cmml">⁢</mo>
            <mi mathcolor="#000000" id="p1.1.m1.1.10.1.4" xref="p1.1.m1.1.10.1.4.cmml">μ</mi>
          </mrow>
        </msub>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
        <and id="p1.1.m1.1.11a.cmml" xref="p1.1.m1.1.11"/>
        <apply id="p1.1.m1.1.11b.cmml" xref="p1.1.m1.1.11">
          <eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
          <apply id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.11.2.1.cmml" xref="p1.1.m1.1.11.2">subscript</csymbol>
            <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑅</ci>
            <apply id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">
              <times id="p1.1.m1.1.2.1.5.cmml" xref="p1.1.m1.1.2.1.5"/>
              <ci id="p1.1.m1.1.2.1.1.cmml" xref="p1.1.m1.1.2.1.1">𝛼</ci>
              <ci id="p1.1.m1.1.2.1.2.cmml" xref="p1.1.m1.1.2.1.2">𝛽</ci>
              <ci id="p1.1.m1.1.2.1.3.cmml" xref="p1.1.m1.1.2.1.3">𝜇</ci>
              <ci id="p1.1.m1.1.2.1.4.cmml" xref="p1.1.m1.1.2.1.4">𝜈</ci>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.11.3.cmml" xref="p1.1.m1.1.11.3">
            <minus id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
            <apply id="p1.1.m1.1.11.3.1.cmml" xref="p1.1.m1.1.11.3.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.11.3.1.1.cmml" xref="p1.1.m1.1.11.3.1">subscript</csymbol>
              <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑅</ci>
              <apply id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">
                <times id="p1.1.m1.1.6.1.5.cmml" xref="p1.1.m1.1.6.1.5"/>
                <ci id="p1.1.m1.1.6.1.1.cmml" xref="p1.1.m1.1.6.1.1">𝛽</ci>
                <ci id="p1.1.m1.1.6.1.2.cmml" xref="p1.1.m1.1.6.1.2">𝛼</ci>
                <ci id="p1.1.m1.1.6.1.3.cmml" xref="p1.1.m1.1.6.1.3">𝜇</ci>
                <ci id="p1.1.m1.1.6.1.4.cmml" xref="p1.1.m1.1.6.1.4">𝜈</ci>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.11c.cmml" xref="p1.1.m1.1.11">
          <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
          <share href="#p1.1.m1.1.11.3.cmml" id="p1.1.m1.1.11d.cmml" xref="p1.1.m1.1.11"/>
          <apply id="p1.1.m1.1.11.4.cmml" xref="p1.1.m1.1.11.4">
            <minus id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
            <apply id="p1.1.m1.1.11.4.1.cmml" xref="p1.1.m1.1.11.4.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.11.4.1.1.cmml" xref="p1.1.m1.1.11.4.1">subscript</csymbol>
              <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑅</ci>
              <apply id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">
                <times id="p1.1.m1.1.10.1.5.cmml" xref="p1.1.m1.1.10.1.5"/>
                <ci id="p1.1.m1.1.10.1.1.cmml" xref="p1.1.m1.1.10.1.1">𝛼</ci>
                <ci id="p1.1.m1.1.10.1.2.cmml" xref="p1.1.m1.1.10.1.2">𝛽</ci>
                <ci id="p1.1.m1.1.10.1.3.cmml" xref="p1.1.m1.1.10.1.3">𝜈</ci>
                <ci id="p1.1.m1.1.10.1.4.cmml" xref="p1.1.m1.1.10.1.4">𝜇</ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle R_{{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}%
\beta}{\color[rgb]{0,0,0}\mu}{\color[rgb]{0,0,0}\nu}}=-R_{{\color[rgb]{0,0,0}%
\beta}{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}\mu}{\color[rgb]{0,0,0}\nu}%
}=-R_{{\color[rgb]{0,0,0}\alpha}{\color[rgb]{0,0,0}\beta}{\color[rgb]{0,0,0}%
\nu}{\color[rgb]{0,0,0}\mu}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimentell; keine Bilder) rendering

MathML (1.57 KB / 270 B) :

R_{α β μ ν} = - R_{β α μ ν} = - R_{α β ν μ}

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>&#x03B1;</mi></mstyle></mrow><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><mo>&#x2212;</mo><msub><mi>R</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="#58429B"><mi>&#x03B1;</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><mo>&#x2212;</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#58429B"><mi>&#x03B1;</mi></mstyle></mrow><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 data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>&#x03BC;</mi></mstyle></mrow></mrow></mrow></msub></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$R$

$α$

$β$

$μ$

$ν$

$R$

$β$

$α$

$μ$

$ν$

$R$

$α$

$β$

$ν$

$μ$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

Suche