CH-manifold

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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.