Killing–Hopf theorem explained

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 and .

Notes and References

1. Book: Lee, John M. . John M. Lee . 2018 . Introduction to Riemannian Manifolds . New York . Springer-Verlag . 348 . 978-3-319-91754-2.