Hyperbolic manifold

This article defines a property that makes sense for a Riemannian metric over a differential manifold

Definition

Symbol-free definition

A Riemannian manifold is said to be hyperbolic if it is complete and has constant sectional curvature equal to -1.

Relation with other properties

Weaker properties

• Negatively curved manifold
• Constant-curvature metric
• Einstein metric
• Constant-scalar curvature metric