Second fundamental form

The additional axiological form

is a boxlike anatomy on the departure even to the apparent that, calm with the aboriginal axiological form, determines the curvatures of curves on the surface. In the appropriate case if (u, v) = (x, y) and the departure even to the apparent at the accustomed point is horizontal, the additional axiological anatomy is about the boxlike allotment of the Taylor amplification of z as a action of x and y.

For a accepted parametric surface, the analogue is added complicated, but the additional axiological anatomy depends alone on the fractional derivatives of adjustment one and two. Its coefficients are authentic to be the projections of the additional fractional derivatives of assimilate the assemblage accustomed agent authentic by the parametrization:

Like the aboriginal axiological form, the additional axiological anatomy may be beheld as a ancestors of symmetric bilinear forms on the departure even at anniversary point of the apparent depending calmly on the point.