Dept. Math, Hokkaido Univ. EPrints Server

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);

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Abstract

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.

Item Type:Preprint
Additional Information:60 copies
Uncontrolled Keywords:Monge-Amp\`{e}re equation, Lagrangian pair, geometric solution, cupidal edge, swallowtail, open umbrella.
Subjects:53-xx DIFFERENTIAL GEOMETRY
58-xx GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS
ID Code:861