Non-transversal intersection curves of hypersurfaces in Euclidean 4-space

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:288

Article

Badr, Sayed Abdel-Naeim¹  Abdel-All, Nassar H.¹  Alessio, Osmar²  Duldul, Mustafa³  Duldul, Bahar Uyar⁴ 

[1] Assiut Univ, Fac Sci, Dept Math, Assiut 71516, Egypt

[2] UFTM Triangulo Mineiro Fed Univ, Inst Exact Sci Nat & Educ, Dept Math, Uberaba, MG, Brazil

[3] Yildiz Tech Univ, Sci & Arts Fac, Dept Math, Istanbul, Turkey

[4] Yildiz Tech Univ, Fac Educ, Dept Math Educ, Istanbul, Turkey

关键词: Implicit-implicit-parametric intersection;    Implicit-parametric-parametric intersection;    Non-transversal intersection;    Curvatures;   

DOI  :  10.1016/j.cam.2015.03.054

来源: Elsevier

【 摘 要 】

In this paper, we consider the problem of how to compute the Frenet apparatus of the non-transversal intersection curves (hyper-curves) of three hypersurfaces (given by their implicit-implicit-parametric and implicit-parametric-parametric equations) in Euclidean 4-space. The non-transversal intersection (in which the normal vectors of the intersecting hypersurfaces are linearly dependent) includes two different cases. In each case, on the contrary to transversal intersections, we face some difficulties even finding the tangential direction. To overcome such difficulties, we give some algorithms for finding all Frenet vectors and curvatures of the intersection curve. Finally, we demonstrate our methods by giving several examples. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free