HORO-FLAT SURFACES ALONG CUSPIDAL EDGES IN THE HYPERBOLIC SPACE


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Title:	HORO-FLAT SURFACES ALONG CUSPIDAL EDGES IN THE HYPERBOLIC SPACE
Authors:	Izumiya, Shyuichi Browse this author →KAKEN DB
	Romero-Fuster, Maria Carmen Browse this author
	Saji, Kentaro Browse this author
	Takahashi, Masatomo Browse this author
Keywords:	cuspidal edges
	flat approximations
	curves on surfaces
	Darboux frame
	horo-flat surfaces
Issue Date:	1-Dec-2020
Publisher:	Worldwide Center of Mathematics
Journal Title:	Journal of Singularities
Volume:	22
Start Page:	40
End Page:	58
Publisher DOI:	10.5427/jsing.2020.22d
Abstract:	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.
Type:	article
URI:	http://hdl.handle.net/2115/79845
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)

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