LOCAL DIFFERENTIAL GEOMETRY OF CUSPIDAL EDGE AND SWALLOWTAIL

Fukui, Toshizumi

Osaka Journal of Mathematics, 2020, 57(4), 961-992

アクセス数:153件（2025-07-05 14:50 集計）

固定URL: https://doi.org/10.18910/77239

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タイトル	LOCAL DIFFERENTIAL GEOMETRY OF CUSPIDAL EDGE AND SWALLOWTAIL
著者	NRID 1000090218892 1000090218892 著者名 Fukui, Toshizumi
抄録	We investigate the local differential geometric invariants of cuspidal edge and swallowtail from the view point of singularity theory. We introduce finite type invariants of such singularities (see Remark 1.5 and Theorem 2.11) based on certain normal forms for cuspidal edge and swallowtail. Then we discuss several geometric aspects based on our normal form. We also present several asymptotic formulas concerning our invariants with respect to Gauss curvature and mean curvature.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	57(4)
ページ	961-992
刊行年月	2020-10
言語	英語
ハンドルURL	https://hdl.handle.net/11094/77239
DOI	https://doi.org/10.18910/77239
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 57, Number 4 （2020-10）

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. 2020, 57(4), p. 961-992
DC.title	LOCAL DIFFERENTIAL GEOMETRY OF CUSPIDAL EDGE AND SWALLOWTAIL
DC.creator	Fukui, Toshizumi
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	2020-10
DCTERMS.abstract	We investigate the local differential geometric invariants of cuspidal edge and swallowtail from the view point of singularity theory. We introduce finite type invariants of such singularities (see Remark 1.5 and Theorem 2.11) based on certain normal forms for cuspidal edge and swallowtail. Then we discuss several geometric aspects based on our normal form. We also present several asymptotic formulas concerning our invariants with respect to Gauss curvature and mean curvature.
DC.identifier	10.18910/77239
DC.format	77239
citation_title	LOCAL DIFFERENTIAL GEOMETRY OF CUSPIDAL EDGE AND SWALLOWTAIL
citation_author	Fukui, Toshizumi
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2020-10
citation_journal_title	Osaka Journal of Mathematics
citation_volume	57
citation_issue	4
citation_firstpage	961
citation_lastpage	992
citation_public_url	https://hdl.handle.net/11094/77239
citation_doi_detail	10.18910/77239
citation_doi	https://doi.org/10.18910/77239