. The curvature of one of these curves, say, the curve (1), is less than that of all other curves obtained by revolving the plane round the normal at
, while the curvature of the second curve (2) is greater than all others. These two curvatures are called the two principal curvatures of the surface at the point
and are designated by
and
respectively.
We then define the total curvature or the Gaussian curvature of the surface at the point