Singularities of improper affine spheres and surfaces of constant Gaussian curvature
Preprint Series # 694
Ishikawa, Go-o and Machida, Yoshinori Singularities of improper affine spheres and surfaces of constant Gaussian curvature. (2005);
We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singlarities appearing in geometric solutions to the equation as well as their duals. We also show the results for surfaces of constant Gaussian curvature and for developable surfaces. In particular we confirm that generic singularities appearing in such a surface are just cuspidal edges and awallowtails.