Killing–Hopf theorem
Characterizes complete connected Riemannian manifolds of constant curvature
From Wikipedia, the free encyclopedia
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.[1] These manifolds are called space forms. The Killing–Hopf theorem was proved by Killing (1891) and Hopf (1926).
