# CH-manifold

From Diffgeom

*This article defines a property that makes sense for a Riemannian metric over a differential manifold*

## Definition

A **CH-manifold** or **Cartan-Hadamard manifold** is a Riemannian manifold that is simply connected, complete, and has nonpositive sectional curvature. By the Cartan-Hadamard theorem, any CH-manifold is diffeomorphic to some real Euclidean space.