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- Cartan–Hadamard_theorem abstract "In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive sectional curvature. The theorem states that the universal cover of such a manifold is diffeomorphic to a Euclidean space via the exponential map at any point. It was first proved by Hans Carl Friedrich von Mangoldt for surfaces in 1881, and independently by Jacques Hadamard in 1898. Élie Cartan generalized the theorem to Riemannian manifolds in 1928 (Helgason 1978; do Carmo 1992; Kobayashi & Nomizu 1969). The theorem was further generalized to a wide class of metric spaces by Mikhail Gromov in 1987; detailed proofs were published by Ballmann (1990) for metric spaces of non-positive curvature and by Alexander & Bishop (1990) for general locally convex metric spaces.".
- Cartan–Hadamard_theorem wikiPageID "11939373".
- Cartan–Hadamard_theorem wikiPageLength "7162".
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- Cartan–Hadamard_theorem wikiPageRevisionID "659558289".
- Cartan–Hadamard_theorem wikiPageWikiLink Aspherical_space.
- Cartan–Hadamard_theorem wikiPageWikiLink CAT(k)_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Category:Metric_geometry.
- Cartan–Hadamard_theorem wikiPageWikiLink Category:Theorems_in_Riemannian_geometry.
- Cartan–Hadamard_theorem wikiPageWikiLink Complete_metric_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Connected_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Connectedness.
- Cartan–Hadamard_theorem wikiPageWikiLink Contractible.
- Cartan–Hadamard_theorem wikiPageWikiLink Contractible_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Convex_function.
- Cartan–Hadamard_theorem wikiPageWikiLink Covering_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Diffeomorphic.
- Cartan–Hadamard_theorem wikiPageWikiLink Diffeomorphism.
- Cartan–Hadamard_theorem wikiPageWikiLink Euclidean_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Exponential_map_(Riemannian_geometry).
- Cartan–Hadamard_theorem wikiPageWikiLink Foundations_of_Differential_Geometry.
- Cartan–Hadamard_theorem wikiPageWikiLink Geodesic.
- Cartan–Hadamard_theorem wikiPageWikiLink Geometric_group_theory.
- Cartan–Hadamard_theorem wikiPageWikiLink Glossary_of_Riemannian_and_metric_geometry.
- Cartan–Hadamard_theorem wikiPageWikiLink Hadamard_manifold.
- Cartan–Hadamard_theorem wikiPageWikiLink Hadamard_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Hans_Carl_Friedrich_von_Mangoldt.
- Cartan–Hadamard_theorem wikiPageWikiLink Hilbert_manifold.
- Cartan–Hadamard_theorem wikiPageWikiLink Intrinsic_metric.
- Cartan–Hadamard_theorem wikiPageWikiLink Jacques_Hadamard.
- Cartan–Hadamard_theorem wikiPageWikiLink Metric_geometry.
- Cartan–Hadamard_theorem wikiPageWikiLink Metric_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Mikhail_Gromov_(mathematician).
- Cartan–Hadamard_theorem wikiPageWikiLink Mikhail_Leonidovich_Gromov.
- Cartan–Hadamard_theorem wikiPageWikiLink Riemannian_geometry.
- Cartan–Hadamard_theorem wikiPageWikiLink Riemannian_manifold.
- Cartan–Hadamard_theorem wikiPageWikiLink Sectional_curvature.
- Cartan–Hadamard_theorem wikiPageWikiLink Simply_connected.
- Cartan–Hadamard_theorem wikiPageWikiLink Simply_connected_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Springer-Verlag.
- Cartan–Hadamard_theorem wikiPageWikiLink Springer_Science+Business_Media.
- Cartan–Hadamard_theorem wikiPageWikiLink Surface.
- Cartan–Hadamard_theorem wikiPageWikiLink Tangent_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Toponogovs_theorem.
- Cartan–Hadamard_theorem wikiPageWikiLink Universal_cover.
- Cartan–Hadamard_theorem wikiPageWikiLink Universal_covering_space.
- Cartan–Hadamard_theorem wikiPageWikiLink Élie_Cartan.
- Cartan–Hadamard_theorem wikiPageWikiLinkText "Cartan–Hadamard theorem".
- Cartan–Hadamard_theorem hasPhotoCollection Cartan–Hadamard_theorem.
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- Cartan–Hadamard_theorem wikiPageUsesTemplate Template:Refend.
- Cartan–Hadamard_theorem subject Category:Metric_geometry.
- Cartan–Hadamard_theorem subject Category:Theorems_in_Riemannian_geometry.
- Cartan–Hadamard_theorem comment "In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive sectional curvature. The theorem states that the universal cover of such a manifold is diffeomorphic to a Euclidean space via the exponential map at any point. It was first proved by Hans Carl Friedrich von Mangoldt for surfaces in 1881, and independently by Jacques Hadamard in 1898.".
- Cartan–Hadamard_theorem label "Cartan–Hadamard theorem".
- Cartan–Hadamard_theorem sameAs Satz_von_Cartan-Hadamard.
- Cartan–Hadamard_theorem sameAs Stelling_van_Cartan-Hadamard.
- Cartan–Hadamard_theorem sameAs Teorema_de_Cartan-Hadamard.
- Cartan–Hadamard_theorem sameAs m.02ryw3j.
- Cartan–Hadamard_theorem sameAs Q5047048.
- Cartan–Hadamard_theorem sameAs Q5047048.
- Cartan–Hadamard_theorem wasDerivedFrom Cartan–Hadamard_theorem?oldid=659558289.
- Cartan–Hadamard_theorem isPrimaryTopicOf Cartan–Hadamard_theorem.