Riemannian manifolds

Hadamard manifold

In mathematics, a Hadamard manifold, named after Jacques Hadamard — more often called a Cartan–Hadamard manifold, after Élie Cartan — is a Riemannian manifold that is complete and simply connected and has everywhere non-positive sectional curvature. By Cartan–Hadamard theorem all Cartan–Hadamard manifolds are diffeomorphic to the Euclidean space Furthermore it follows from the Hopf–Rinow theorem that every pairs of points in a Cartan–Hadamard manifold may be connected by a unique geodesic segment. Thus Cartan–Hadamard manifolds are some of the closest relatives of (Wikipedia).

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Related pages

Hyperbolic space | Cartan–Hadamard theorem | Sectional curvature | Mathematics | Hopf–Rinow theorem | Jacques Hadamard | Riemannian manifold | Euclidean space | Complete metric space | Élie Cartan | Simply connected space