 The notion of curvature extends to the category of geodesic metric spaces, where one can use comparison triangles to quantify the curvature of a space; in this context, non-positively curved spaces are known as (locally) CAT(0) spaces.If formula_1 is a closed, orientable Riemann surface then it follows from the Uniformization theorem that formula_1 may be endowed with a complete Riemannian metric with constant Gaussian curvature of either formula_3, formula_4 or formula_5.As a result of the Gauss–Bonnet theorem one can determine that the surfaces which have a Riemannian metric of constant curvature formula_6 formula_7 i.e.