The model shows the neighbourhood of a parabolic point P with the normal of the surface. One of the principal circles of curvature is degenerated to a straight line.

At the same time the portrayed figure represents that in a general parabolic point P osculating vertex paraboloid (a parabolic cylinder). Indeed the real parallel intersections to the tangential plane in the point P have the appearance of the Dupian indicatrix in P.

Surface areas with solely parabolic surface points are called curved and are developable. The Gaussian curvature is zero.

In general the elliptic and the hyperbolic points of a surface fulfill certain connected areas, that are separated by border lines of parabolic points.