Soul theorem

In mathematics, the soul theorem is a classical theorem of Riemannian geometry. It can be stated as follows:

References

• Cheeger, Jeff; Gromoll, Detlef On the structure of complete manifolds of nonnegative curvature. Ann. of Math. (2) 96 (1972), 413--443.
• Gromoll, Detlef; Meyer, Wolfgang On complete open manifolds of positive curvature. Ann. of Math. (2) 90 1969 75--90.
• Perelman, G. Proof of the soul conjecture of Cheeger and Gromoll. J. Differential Geom. 40 (1994), no. 1, 209--212.