 Hyperbolic metric space

For $\delta \ge 0$, a geodesic metric space is $\delta$-hyperbolic when each side of every metric geodesic triangle lies in the closed $\delta$-neighbourhood of the other two sides.

A hyperbolic metric space is a geometric structure in which the geometry is shaped by hyperbolic properties. More formally, a hyperbolic space is a geodesic metric space that satisfies certain conditions characterizing hyperbolic geometry, a non-Euclidean geometry. ### Key Characteristics: 1. **Negative Curvature**: Hyperbolic metric spaces have negative curvature.