ON THE DEVELOPABLE RULED SURFACES OF LOW SMOOTHNESS

The classical description of the structure of developable surfaces of torse type is formally possible only starting with C(3)-smoothness. We consider developable surfaces of class C(2) and show that the directions of their generators at the boundary points of a surface belong to the tangent cone of the boundary curve. In analytical terms we give a necessary and sufficient condition for C(1)-smooth surfaces with locally Euclidean metric to belong to the class of the so-called normal developable surfaces introduced by Burago and Shefel'.