 From this point of view, rolling the tangent plane over a surface defines an affine connection on the surface (it provides an example of parallel transport along a curve), and a developable surface is one for which this connection is flat.More generally any flat Cartan connection on a manifold defines a development of that manifold onto the model space.Perhaps the most famous example is the development of conformally flat "n"-manifolds, in which the model-space is the "n"-sphere.