Differential geometry of transversal intersection curves of hypersurfaces in ℝ<sup>5</sup>

Lone, Mohamd Saleem; Aléssio, Osmar; Jamali, Mohammed; Shahid, Mohammad Hasan

doi:10.1080/1726037x.2017.1411042

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2021

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“…Differential geometry of intersection curves of two parametric surfaces in Euclidean 3-space has been studied by some authors using different methods 260 MUSTAFA D ÜLD ÜL AND B. MERIH ÖZC ¸ETIN [10,21]. These studies have been extended to E 4 for the intersection of three parametric hypersurfaces [6,9,10,14] and to E 5 for the intersection of four parametric hypersurfaces [15]. Since surfaces can also be defined by their implicit equations, differential geometry of the intersection curve of two implicit surfaces has been studied in E 3 by [2,12,20,21] and of three implicit hypersurfaces has been studied in E 4 by [3,4,7,14,19].…”

Section: Introductionmentioning

confidence: 99%

Intersection curve of two parametric surfaces in Euclidean n-space

Düldül

Özçetin

2021

ACUTM

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The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.

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