Cartan-Hadamard theorem

This article describes a result related to the sectional curvature of a Riemannian manifold

This result relates information on curvature to information on topology of a manifold

This article makes a prediction about the universal cover of a manifold based on given data at the level of a:[[{{{1}}}]][[Category: Results predicting the universal cover at the level of {{{1}}}]]

Statement

Any negatively curved manifold, viz any manifold which has negative sectional curvature everywhere, has the property that its universal cover is diffeomorphic to real Euclidean space.