About: Killing–Hopf theorem

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In geometry, the Killing–Hopf theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space, or hyperbolic space by a group acting freely and properly discontinuously. These manifolds are called space forms. The Killing–Hopf theorem was proved by Killing and Hopf.

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  • In geometry, the Killing–Hopf theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space, or hyperbolic space by a group acting freely and properly discontinuously. These manifolds are called space forms. The Killing–Hopf theorem was proved by Killing and Hopf. (en)
  • Inom matematiken är Killing–Hopfs sats ett resultat som säger att en fullständig sammanhängande Riemannmångfald av konstant krökning är isometrisk till ett av en sfär, ett Euklidiskt rum eller ett med en grupp som verkar fritt och . Dessa mångfalder är kända som . Killing–Hopfs sats bevisades av Killing och Hopf. (sv)
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  • In geometry, the Killing–Hopf theorem states that complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space, or hyperbolic space by a group acting freely and properly discontinuously. These manifolds are called space forms. The Killing–Hopf theorem was proved by Killing and Hopf. (en)
  • Inom matematiken är Killing–Hopfs sats ett resultat som säger att en fullständig sammanhängande Riemannmångfald av konstant krökning är isometrisk till ett av en sfär, ett Euklidiskt rum eller ett med en grupp som verkar fritt och . Dessa mångfalder är kända som . Killing–Hopfs sats bevisades av Killing och Hopf. (sv)
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  • Killing–Hopf theorem (en)
  • Killing–Hopfs sats (sv)
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