Soul theorem

Statement

Any open Riemannian manifold $(M,g)$ with nonnegative sectional curvature contains a compact totally geodesic submanifold $S$ (called the soul), such that $M$ is diffeomorphic to the normal bundle on $S$, viz $\nu (S)$.

References

• Improving the metric in an open manifold with nonnegative curvature by Luis Guijarro, Proceedings of the American Mathematical Society, Volume 126, Number 5, May 1998, Pages 1541-1545

External links

• Improving the metric in an open manifold with nonnegative curvature