# Negatively curved manifold

From Diffgeom

Thiss article defines a property that can be evaluated for a differential manifold, invariant under diffeomorphisms

View other properties of differential manifolds

## Contents

## 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 ).