Gaussian curvature
There are other surfaces which have constant positive Gaussian curvature. Manfredo do Carmo considers surfaces of revolution formula_5 where formula_6, and formula_7 (an incomplete Elliptic integral of the second kind). These surfaces all have constant Gaussian curvature of 1, but, for formula_8 either have a boundary or a singular point. do Carmo also gives three different examples of surface with constant negative Gaussian curvature, one of which is pseudosphere.