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Characterizes complete connected Riemannian manifolds of constant curvature
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 (
1891) and
Hopf (
1926).
-
Hopf, Heinz (1926), "Zum Clifford-Kleinschen Raumproblem",
Mathematische Annalen, 95 (1): 313–339,
doi:
10.1007/BF01206614,
ISSN
0025-5831
- Killing, Wilhelm (1891), "Ueber die Clifford-Klein'schen Raumformen",
Mathematische Annalen, 39 (2): 257–278,
doi:
10.1007/BF01206655,
ISSN
0025-5831
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