Negatively curved manifold

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.

Facts

Cartan-Hadamard theorem

The Cartan-Hadamard theorem states that the universal cover of any negatively curved manfiold is diffeomorphic to Euclidean space (viz $\mathbb {R} ^{n}$).