ON THE FLAT GEOMETRY OF THE CUSPIDAL EDGE

Oset Sinha, Raúl; Tari, Farid

doi:https://doi.org/10.18910/70079

ON THE FLAT GEOMETRY OF THE CUSPIDAL EDGE

Oset Sinha, Raúl; Tari, Farid

Osaka Journal of Mathematics, 2018, 55(3), 393-421

アクセス数:74件（2025-05-17 08:52 集計）

固定URL: https://doi.org/10.18910/70079

閲覧可能ファイル

ファイル	フォーマット	利用条件	サイズ	閲覧回数	利用開始日	説明	information
ojm55_03_393	pdf	なし	1.98 MB	81	2018.07.18

論文情報

ファイル出力 EndNote Basic出力 Mendeley出力

タイトル	ON THE FLAT GEOMETRY OF THE CUSPIDAL EDGE
著者	著者名 Oset Sinha, Raúl
著者	著者名 Tari, Farid
抄録	We study the geometry of the cuspidal edge M in ℝ³ derived from its contact with planes and lines (referred to as flat geometry). The contact of M with planes is measured by the singularities of the height functions on M. We classify submersions on a model of M by diffeomorphisms and recover the contact of M with planes from that classification. The contact of M with lines is measured by the singularities of orthogonal projections of M. We list the generic singularities of the projections and obtain the generic deformations of the apparent contour (profile) when the direction of projection varies locally in S². We also relate the singularities of the height functions and of the projections to some geometric invariants of the cuspidal edge.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	55(3)
ページ	393-421
刊行年月	2018-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/70079
DOI	https://doi.org/10.18910/70079
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 55, Number 3 （2018-7）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2018, 55(3), p. 393-421
DC.title	ON THE FLAT GEOMETRY OF THE CUSPIDAL EDGE
DC.creator	Oset Sinha, Raúl
DC.creator	Tari, Farid
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2018-07
DCTERMS.abstract	We study the geometry of the cuspidal edge M in ℝ³ derived from its contact with planes and lines (referred to as flat geometry). The contact of M with planes is measured by the singularities of the height functions on M. We classify submersions on a model of M by diffeomorphisms and recover the contact of M with planes from that classification. The contact of M with lines is measured by the singularities of orthogonal projections of M. We list the generic singularities of the projections and obtain the generic deformations of the apparent contour (profile) when the direction of projection varies locally in S². We also relate the singularities of the height functions and of the projections to some geometric invariants of the cuspidal edge.
DC.identifier	10.18910/70079
DC.format	70079
citation_title	ON THE FLAT GEOMETRY OF THE CUSPIDAL EDGE
citation_author	Oset Sinha, Raúl
citation_author	Tari, Farid
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2018-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	55
citation_issue	3
citation_firstpage	393
citation_lastpage	421
citation_public_url	https://hdl.handle.net/11094/70079
citation_doi_detail	10.18910/70079
citation_doi	https://doi.org/10.18910/70079

ON THE FLAT GEOMETRY OF THE CUSPIDAL EDGE

閲覧可能ファイル

論文情報

論文詳細を表示