Negatively curved manifold

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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 M 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 \mathbb{R}^n).