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Singularities of improper affine spheres and surfaces of constant Gaussian curvature

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Title: Singularities of improper affine spheres and surfaces of constant Gaussian curvature
Authors: Ishikawa, Go-o Browse this author →KAKEN DB
Machida, Yoshinori Browse this author
Keywords: Monge–Ampère equation
Lagrangian pair
geometric solution
cuspidal edge
open umbrella
Issue Date: Mar-2006
Publisher: World Scientific
Journal Title: International journal of mathematics
Volume: 17
Issue: 3
Start Page: 269
End Page: 293
Publisher DOI: 10.1142/S0129167X06003485
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
Rights: copyright(c)2006 for World Scientific
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 石川 剛郎

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