  Any surface can be foliated into equipotential hypersurfaces of the level
sets. A current result is that the contours are the progressing wave fronts of
a certain hyperbolic partial differential equation, a wave equation. It is
connected with the gradient lines, as well as with a corresponding eikonal
equation. The level of a surface point, seen as an additional coordinate, plays
the central role in this treatment. A wave solution can be a sharp front. Here
the validity of the Huygens' principle (HP) is of interest: there is no wake of
the wave solutions in every dimension, if a special Cauchy initial value
problem is posed. Additionally, there is no distinction into odd or even
dimensions. To compare this with Hadamard's 'minor premise' for a strong HP, we
calculate differential geometric objects like Christoffel symbols, curvature
tensors and geodesic lines, to test the validity of the strong HP. However, for
the differential equation for level sets, the main criteria are not fulfilled
for the strong HP in the sense of Hadamard's 'minor premise'.
