Differential geometry of non-transversal intersection curves of three implicit hypersurfaces in Euclidean 4-space
type: Item
instance of: scholarly article
title: Differential geometry of non-transversal intersection curves of three implicit hypersurfaces in Euclidean 4-space
zbMATH Open document ID: 1350.53005
author: B. Uyar Düldül
author: Nassar H. Abdel-All
author: Sayed Abdel-Naeim Badr
author: Osmar Aléssio
author: Mustafa Düldül
published in: Journal of Computational and Applied Mathematics
publication date: 2016-08-16T00:00:00Z
review text: The authors consider non-transversal intersection curves of three implicit hypersurfaces in Euclidean 4-space. The intersection is called non-transversal when the normal vectors are linearly dependent at the intersection point. In Euclidean 4-space, four kinds of intersection exist. Non-transversal intersections of three hypersurfaces with normal vectors \(N_i\) at the point \(p\) occur in two different cases, namely almost tangential intersection and tangential intersection, i.e., when the dimension of \(\mathrm{span}(N_1(p), N_2(p), N_3(p))\) equals 2 or 1, respectively. Here these two cases are discussed. Algorithms are given to find the Frenet vectors and the curvature of the non-transversal intersection curves. At the end, the authors give several interesting special examples.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 6617288
zbMATH Keywords: intersection
zbMATH Keywords: tangential intersection
zbMATH Keywords: geometric properties
zbMATH Keywords: non-transversal intersection
zbMATH Keywords: implicit curves
Wikidata QID: Q115359817
reviewed by: Johannes Böhm
MaRDI profile type: Publication
full work available at URL: j.cam.2016.05.011
OpenAlex ID: W4214821422
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DOI: 10.1016/J.CAM.2016.05.011
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description: scientific article; zbMATH DE number 6617288