killing, hopf, theorem, geometry, states, that, complete, connected, riemannian, manifolds, constant, curvature, isometric, quotient, sphere, euclidean, space, hyperbolic, space, group, acting, freely, properly, discontinuously, these, manifolds, called, space. 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 EditHopf 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 This geometry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Killing Hopf theorem amp oldid 1053923079, wikipedia, wiki, book, books, library,
