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Hokkaido University Preprint Series in Mathematics >
Singularities of improper affine spheres and surfaces of constant Gaussian curvature
| Title: | Singularities of improper affine spheres and surfaces of constant Gaussian curvature |
| Authors: | Ishikawa, Go-o Browse this author | | Machida, Yoshinori Browse this author |
| Keywords: | Monge-Ampére equation | | Lagrangian pair | | geometric solution | | cuspidal edge | | swallowtail | | open umbrella |
| Issue Date: | 2005 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 694 |
| Start Page: | 1 |
| End Page: | 20 |
| Abstract: | We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities 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 swallowtails. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69499 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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