Singularities of improper affine spheres and surfaces of constant Gaussian curvature

Ishikawa, Go-o; Machida, Yoshinori

Hokkaido University Preprint Series in Mathematics, 2005, 694, 1-20

Permalink : https://doi.org/10.14943/83845

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アクセス権	open access
DOI	https://doi.org/10.14943/83845
URI	https://hdl.handle.net/2115/69499
タイトル	Singularities of improper affine spheres and surfaces of constant Gaussian curvature
著者	著者名 Ishikawa, Go-o
著者	著者名 Machida, Yoshinori
言語	英語
キーワード	Monge-Ampére equation
	Lagrangian pair
	geometric solution
	cuspidal edge
	swallowtail
	open umbrella
発行日	2005
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	694
ページ	1-20
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record