@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:-NBDBFH2B-5
  skos:prefLabel "mathematical physics"@en, "physique mathématique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-XWWVH3PC-T .

psr:-SDZH6QJN-Z
  skos:prefLabel "transformation géométrique"@fr, "geometric transformation"@en ;
  a skos:Concept ;
  skos:narrower psr:-XWWVH3PC-T .

psr:-XWWVH3PC-T
  skos:narrower psr:-RJD29DDL-S, psr:-SDBF6PF1-T, psr:-M8RJGTGT-V, psr:-XVW7H807-8 ;
  skos:definition """En mathématiques, et plus précisément en géométrie et en analyse complexe, une transformation conforme est une bijection qui conserve localement les angles, c'est-à-dire qui se comporte au voisinage de chaque point où elle est définie presque comme une similitude. Dans le plan, les transformations conformes qui conservent les angles orientés ont une telle utilité qu'il est fréquent qu'elles soient les seules baptisées du terme de conformes. Elles se confondent alors avec les bijections holomorphes. Les transformations conformes indirectes sont, dans ce cas, appelées transformations anticonformes. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Transformation_conforme">https://fr.wikipedia.org/wiki/Transformation_conforme</a>)"""@fr, """In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let <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 U}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>U</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle U}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.783ex; height:2.176ex;" alt="U"></span> 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 V}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>V</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle V}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="V"></span> be open subsets of <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 \\\\mathbb {R} ^{n}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msup>
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="double-struck">R</mi>
         </mrow>
         <mrow class="MJX-TeXAtom-ORD">
         <mi>n</mi>
         </mrow>
         </msup>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{n}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="\\\\mathbb {R} ^{n}"></span>. A function <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 f:U\\	o V}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>f</mi>
         <mo>:</mo>
         <mi>U</mi>
         <mo stretchy="false">→<!-- → --></mo>
         <mi>V</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle f:U\\	o V}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99d431c81a43bf61447672a1c6e62d56fc73026a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.4ex; height:2.509ex;" alt="{\\\\displaystyle f:U\\	o V}"></span> is called <b>conformal</b> (or <b>angle-preserving</b>) at a point <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 u_{0}\\\\in U}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msub>
         <mi>u</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mn>0</mn>
         </mrow>
         </msub>
         <mo>∈<!-- ∈ --></mo>
         <mi>U</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle u_{0}\\\\in U}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/133e383f80a11def53dfb9316d0d4f71d32b20da" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.007ex; height:2.509ex;" alt="{\\\\displaystyle u_{0}\\\\in U}"></span> if it preserves angles between directed curves through <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 u_{0}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msub>
         <mi>u</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mn>0</mn>
         </mrow>
         </msub>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle u_{0}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c7425f9c7ab645587060423c0af62f8a61fbc65" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="u_{0}"></span>, as well as preserving orientation. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Conformal_map">https://en.wikipedia.org/wiki/Conformal_map</a>)"""@en ;
  skos:broader psr:-BK1H4W0H-M, psr:-RXVD8XPD-V, psr:-SDZH6QJN-Z, psr:-NBDBFH2B-5 ;
  skos:prefLabel "transformation conforme"@fr, "conformal map"@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Conformal_map>, <https://fr.wikipedia.org/wiki/Transformation_conforme> ;
  skos:inScheme psr: ;
  dc:modified "2023-08-10"^^xsd:date ;
  a skos:Concept .

psr:-RXVD8XPD-V
  skos:prefLabel "géométrie conforme"@fr, "conformal geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-XWWVH3PC-T .

psr:-RJD29DDL-S
  skos:prefLabel "Joukowsky transform"@en, "transformation de Joukovsky"@fr ;
  a skos:Concept ;
  skos:broader psr:-XWWVH3PC-T .

psr:-M8RJGTGT-V
  skos:prefLabel "quasiconformal mapping"@en, "application quasi conforme"@fr ;
  a skos:Concept ;
  skos:broader psr:-XWWVH3PC-T .

psr: a skos:ConceptScheme .
psr:-BK1H4W0H-M
  skos:prefLabel "fonction complexe"@fr, "complex function"@en ;
  a skos:Concept ;
  skos:narrower psr:-XWWVH3PC-T .

psr:-XVW7H807-8
  skos:prefLabel "planar Riemann surface"@en, "surface de Riemann planaire"@fr ;
  a skos:Concept ;
  skos:broader psr:-XWWVH3PC-T .

psr:-SDBF6PF1-T
  skos:prefLabel "Cayley transform"@en, "transformation de Cayley"@fr ;
  a skos:Concept ;
  skos:broader psr:-XWWVH3PC-T .