HORO-FLAT SURFACES ALONG CUSPIDAL EDGES IN THE HYPERBOLIC SPACE

Izumiya, Shyuichi; Romero-Fuster, Maria Carmen; Saji, Kentaro; Takahashi, Masatomo

HORO-FLAT SURFACES ALONG CUSPIDAL EDGES IN THE HYPERBOLIC SPACE

Izumiya, Shyuichi; Romero-Fuster, Maria Carmen; Saji, Kentaro et al.

Journal of Singularities, 2020, 22, 40-58

Permalink : https://hdl.handle.net/2115/79845

このアイテムのアクセス数:681件（2026-08-19 15:39 集計）

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https://doi.org/10.5427/jsing.2020.22d			11

論文情報

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アクセス権	open access
URI	https://hdl.handle.net/2115/79845
タイトル	HORO-FLAT SURFACES ALONG CUSPIDAL EDGES IN THE HYPERBOLIC SPACE
著者	Izumiya, Shyuichi ; Romero-Fuster, Maria Carmen ; Saji, Kentaro ; Takahashi, Masatomo
e-Rad_Researcher 80127422 著者名 Izumiya, Shyuichi
著者名 Romero-Fuster, Maria Carmen
著者名 Saji, Kentaro
著者名 Takahashi, Masatomo
言語	英語
キーワード	cuspidal edges
	flat approximations
	curves on surfaces
	Darboux frame
	horo-flat surfaces
発行日	2020-12-01
出版者	Worldwide Center of Mathematics
収録物名	Journal of Singularities
巻(号)	22
ページ	40-58
抄録	There are two important classes of surfaces in the hyperbolic space. One of class consists of extrinsic flat surfaces, which is an analogous notion to developable surfaces in the Euclidean space. Another class consists of horo-flat surfaces, which are given by one-parameter families of horocycles. We use the Legendrian dualities between hyperbolic space, de Sitter space and the lightcone in the Lorentz-Minkowski 4-space in order to study the geometry of flat surfaces defined along the singular set of a cuspidal edge in the hyperbolic space. Such flat surfaces can be considered as flat approximations of the cuspidal edge. We investigate the geometrical properties of a cuspidal edge in terms of the special properties of its flat approximations.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
PISSN	1949-2006
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.5427/jsing.2020.22d