 In dimensions greater than formula_12 the Mostow–Prasad rigidity theorem ensures that a hyperbolic manifold of finite area has a unique complete hyperbolic metric so the study of hyperbolic geometry in this setting is integral to the study of topology.In an arbitrary geodesic metric space the notions of being Gromov hyperbolic or of being a CAT(0) space generalise the notion that on a Riemann surface of non-positive curvature, triangles whose sides are geodesics appear "thin" whereas in settings of positive curvature they appear "fat".This notion of non-positive curvature allows the notion of non-positive curvature is most commonly applied to graphs and is therefore of great use in the fields of combinatorics and geometric group theory.