@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-L84V4M82-V
  skos:prefLabel "isomorphisme"@fr, "isomorphism"@en ;
  a skos:Concept ;
  skos:narrower psr:-S909F0LS-C .

psr:-S909F0LS-C
  skos:definition """In mathematics—more specifically, in differential geometry—the <b>musical isomorphism</b> (or <b>canonical isomorphism</b>) is an isomorphism between the tangent bundle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathrm {T} M}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">T</mi>
         </mrow>
         <mi>M</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {T} M}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90396560b7491143b445eb6d5263de21a938e387" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.12ex; height:2.176ex;" alt="{\\\\displaystyle \\\\mathrm {T} M}"></span> and the cotangent bundle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathrm {T} ^{*}M}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msup>
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">T</mi>
         </mrow>
         <mrow class="MJX-TeXAtom-ORD">
         <mo>∗<!-- ∗ --></mo>
         </mrow>
         </msup>
         <mi>M</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {T} ^{*}M}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea4fc712ed59e46885b3b797c26c51e0fe7df4c9" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.175ex; height:2.343ex;" alt="{\\\\displaystyle \\\\mathrm {T} ^{*}M}"></span> of a pseudo-Riemannian manifold induced by its metric tensor. There are similar isomorphisms on symplectic manifolds. The term <i>musical</i> refers to the use of the symbols <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\lat }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi mathvariant="normal">♭<!-- ♭ --></mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\lat }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a36cd97c6cdf0ae5b1810aa7a8769a71701c900" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.905ex; height:2.343ex;" alt="\\lat "></span> (flat) and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\sharp }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi mathvariant="normal">♯<!-- ♯ --></mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sharp }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec62aeac3396a6355d56723cbc51ddf01bb90883" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:0.905ex; height:2.843ex;" alt="\\\\sharp "></span> (sharp).
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Musical_isomorphism">https://en.wikipedia.org/wiki/Musical_isomorphism</a>)"""@en, """En mathématiques, plus précisément en géométrie différentielle, l'isomorphisme musical (ou isomorphisme canonique ) est un isomorphisme entre le fibré tangent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathrm {T} M}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">T</mi>
         </mrow>
         <mi>M</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {T} M}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90396560b7491143b445eb6d5263de21a938e387" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.12ex; height:2.176ex;" alt="{\\\\displaystyle \\\\mathrm {T} M}"></span> et le fibré cotangent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathrm {T} ^{*}M}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msup>
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">T</mi>
         </mrow>
         <mrow class="MJX-TeXAtom-ORD">
         <mo>∗<!-- ∗ --></mo>
         </mrow>
         </msup>
         <mi>M</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {T} ^{*}M}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea4fc712ed59e46885b3b797c26c51e0fe7df4c9" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.175ex; height:2.343ex;" alt="{\\\\displaystyle \\\\mathrm {T} ^{*}M}"></span> d'une variété pseudo-riemannienne induite par son tenseur métrique. Il existe des isomorphismes similaires sur les variétés symplectiques. Le terme <i>musical</i> fait référence à l'utilisation des symboles <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\lat }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi mathvariant="normal">♭<!-- ♭ --></mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\lat }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a36cd97c6cdf0ae5b1810aa7a8769a71701c900" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.905ex; height:2.343ex;" alt="\\lat "></span> (bémol) et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\sharp }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi mathvariant="normal">♯<!-- ♯ --></mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sharp }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec62aeac3396a6355d56723cbc51ddf01bb90883" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:0.905ex; height:2.843ex;" alt="\\\\sharp "></span> (dièse).
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Isomorphisme_musical">https://fr.wikipedia.org/wiki/Isomorphisme_musical</a>)"""@fr ;
  a skos:Concept ;
  skos:broader psr:-L84V4M82-V, psr:-P43HJWNV-X, psr:-TTBXXW26-C ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Musical_isomorphism>, <https://fr.wikipedia.org/wiki/Isomorphisme_musical> ;
  skos:prefLabel "musical isomorphism"@en, "isomorphisme musical"@fr ;
  dc:modified "2023-06-29"^^xsd:date ;
  dc:created "2023-06-29"^^xsd:date ;
  skos:altLabel "canonical isomorphism"@en ;
  skos:inScheme psr: .

psr: a skos:ConceptScheme .
psr:-P43HJWNV-X
  skos:prefLabel "symplectic geometry"@en, "géométrie symplectique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-S909F0LS-C .

psr:-TTBXXW26-C
  skos:prefLabel "Riemannian geometry"@en, "géométrie riemannienne"@fr ;
  a skos:Concept ;
  skos:narrower psr:-S909F0LS-C .