@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr: a skos:ConceptScheme .
psr:-TTBXXW26-C
  skos:prefLabel "Riemannian geometry"@en, "géométrie riemannienne"@fr ;
  a skos:Concept ;
  skos:narrower psr:-ZMXS7MB5-V .

psr:-ZMXS7MB5-V
  skos:definition """En géométrie riemannienne, le lemme de Gauss permet de comprendre l'application exponentielle comme une isométrie radiale. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Lemme_de_Gauss_(g%C3%A9om%C3%A9trie_riemannienne)">https://fr.wikipedia.org/wiki/Lemme_de_Gauss_(g%C3%A9om%C3%A9trie_riemannienne)</a>)"""@fr, """In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let <i>M</i> be a Riemannian manifold, equipped with its Levi-Civita connection, and <i>p</i> a point of <i>M</i>. The exponential map is a mapping from the tangent space at <i>p</i> to <i>M</i>:
         
         <dl><dd><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 {exp} :T_{p}M\\	o M}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">e</mi>
         <mi mathvariant="normal">x</mi>
         <mi mathvariant="normal">p</mi>
         </mrow>
         <mo>:</mo>
         <msub>
         <mi>T</mi>
         <mrow class="MJX-TeXAtom-ORD">
         <mi>p</mi>
         </mrow>
         </msub>
         <mi>M</mi>
         <mo stretchy="false">→<!-- → --></mo>
         <mi>M</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {exp} :T_{p}M\\	o M}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f4001dfb1142c053ea17c51b034256bf6b46991" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:16.405ex; height:2.843ex;" alt="{\\\\mathrm  {exp}}:T_{p}M\\	o M"></span></dd></dl>
         which is a diffeomorphism in a neighborhood of zero. Gauss' lemma asserts that the image of a sphere of sufficiently small radius in <i>T</i><sub>p</sub><i>M</i> under the exponential map is perpendicular to all geodesics originating at <i>p</i>. The lemma allows the exponential map to be understood as a radial isometry, and is of fundamental importance in the study of geodesic convexity and normal coordinates. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Gauss%27s_lemma_(Riemannian_geometry)">https://en.wikipedia.org/wiki/Gauss%27s_lemma_(Riemannian_geometry)</a>)"""@en ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:broader psr:-TTBXXW26-C ;
  skos:prefLabel "Gauss's lemma"@en, "lemme de Gauss"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Lemme_de_Gauss_(g%C3%A9om%C3%A9trie_riemannienne)>, <https://en.wikipedia.org/wiki/Gauss%27s_lemma_(Riemannian_geometry)> .