Hadamard-Cartan theorem
= Hadamard-Cartan theorem
{c}
{wiki=Cartan–Hadamard_theorem}
On a complete connected Riemannian manifold of nonpositive sectional curvature, the exponential map at every point is a covering map. If the manifold is simply connected, each exponential map is a diffeomorphism from a tangent space onto the manifold.