Cartan–Hadamard theorem
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 . The theorem was further generalized to a wide class of metric spaces by Mikhail Gromov in 1987; detailed proofs were published by for metric spaces of non-positive curvature and by for general locally convex metric spaces.
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Cartan–Hadamard theorem
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 . The theorem was further generalized to a wide class of metric spaces by Mikhail Gromov in 1987; detailed proofs were published by for metric spaces of non-positive curvature and by for general locally convex metric spaces.
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En géométrie riemannienne, le ...... éral dans le cadre riemannien.
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In de Riemann-meetkunde, een d ...... gemene lokaal convexe ruimten.
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In der Mathematik ist der Satz ...... iemannsche Mannigfaltigkeiten.
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In mathematics, the Cartan–Had ...... locally convex metric spaces.
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O Teorema de Cartan-Hadamard é ...... ublicadas por Ballmann (1990).
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Теорема Адамара — Картана — тв ...... оведений Картаном в 1928 році.
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Теорема Адамара — Картана — ут ...... морфно евклидову пространству.
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En géométrie riemannienne, le ...... éral dans le cadre riemannien.
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In de Riemann-meetkunde, een d ...... ntiële afbeelding op elk punt.
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In der Mathematik ist der Satz ...... iemannsche Mannigfaltigkeiten.
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In mathematics, the Cartan–Had ...... locally convex metric spaces.
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O Teorema de Cartan-Hadamard é ...... ublicadas por Ballmann (1990).
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Теорема Адамара — Картана — тв ...... оведений Картаном в 1928 році.
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Теорема Адамара — Картана — ут ...... морфно евклидову пространству.
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Cartan–Hadamard theorem
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Satz von Cartan-Hadamard
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Stelling van Cartan-Hadamard
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Teorema de Cartan-Hadamard
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Théorème de Cartan-Hadamard
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Теорема Адамара - Картана
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Теорема Адамара — Картана
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