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Singularities of improper affine spheres and surfaces of constant Gaussian curvature

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83845

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
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

Submitter: 数学紀要登録作業用

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