Negatively curved manifold: Difference between revisions
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===Cartan-Hadamard theorem=== | ===Cartan-Hadamard theorem=== | ||
The Cartan-Hadamard theorem states that the universal cover of any negatively curved manfiold is diffeomorphic to Euclidean | The Cartan-Hadamard theorem states that the universal cover of any negatively curved manfiold is diffeomorphic to Euclidean space (viz <math>\mathbb{R}^n</math>). | ||
Revision as of 13:27, 7 March 2007
Thiss article defines a property that can be evaluated for a differential manifold, invariant under diffeomorphisms
View other properties of differential manifolds
Definition
Symbol-free definition
A differential manifold is said to be negatively curved if it can be equipped with a Riemannian metric with negative sectional curvature.
Definition with symbols
Facts
Cartan-Hadamard theorem
The Cartan-Hadamard theorem states that the universal cover of any negatively curved manfiold is diffeomorphic to Euclidean space (viz ).
