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Concept information

geometry > differential geometry > Poincaré-Hopf theorem
topology > differential topology > Poincaré-Hopf theorem

Terme préférentiel

Poincaré-Hopf theorem  

Définition(s)

  • In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used in differential topology. It is named after Henri Poincaré and Heinz Hopf. The Poincaré–Hopf theorem is often illustrated by the special case of the hairy ball theorem, which simply states that there is no smooth vector field on an even-dimensional n-sphere having no sources or sinks.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Hopf_theorem)

Concept(s) générique(s)

Synonyme(s)

  • Hopf index theorem
  • Poincaré-Hopf index formula
  • Poincaré-Hopf index theorem

Traductions

URI

http://data.loterre.fr/ark:/67375/PSR-VHF8WBJK-0

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RDF/XML TURTLE JSON-LD Date de création 02/08/2023, dernière modif. 24/08/2023