= Cartan–Hadamard theorem
{wiki=Cartan–Hadamard_theorem}
The Cartan-Hadamard theorem is a result in differential geometry, particularly concerning the geometry of Riemannian manifolds. It establishes conditions under which a complete Riemannian manifold without boundary is diffeomorphic to either the Euclidean space or has certain geometric properties related to curvature. Specifically, the theorem states that: If \\( M \\) is a complete, simply connected Riemannian manifold with non-positive sectional curvature (i.e.
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