Killing–Hopf theorem

Killing–Hopf theorem 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).

References Hopf, Heinz (1926), "Zum Clifford-Kleinschen Raumproblem", Anais Matemáticos, 95 (1): 313–339, doi:10.1007/BF01206614, ISSN 0025-5831 Killing, Guilherme (1891), "Ueber die Clifford-Klein'schen Raumformen", Anais Matemáticos, 39 (2): 257-278, doi:10.1007/BF01206655, ISSN 0025-5831 This geometry-related article is a stub. Você pode ajudar a Wikipédia expandindo-a.

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