Differential geometry of non-transversal intersection curves of three implicit hypersurfaces in Euclidean 4-space

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:308

Article

Alessio, O.¹  Duldul, M.²  Duldul, B. Uyar³  Abdel-All, Nassar H.⁴  Badr, Sayed Abdel-Naeim⁴ 

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

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

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

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

关键词: Implicit-implicit-implicit intersection;    Tangential intersection;    Geometric properties;    Non-transversal intersection;    Implicit curves;   

DOI  :  10.1016/j.cam.2016.05.011

来源: Elsevier

【 摘 要 】

The aim of this paper is to compute all the Frenet apparatus of non-transversal intersection curves (hyper-curves) of three implicit hypersurfaces in Euclidean 4-space. The tangential direction at a transversal intersection point can be computed easily, but at a non-transversal intersection point, it is difficult to calculate even the tangent vector. If three normal vectors are parallel at a point, the intersection is tangential intersection; and if three normal vectors are not parallel but are linearly dependent at a point, we have almost tangential intersection at the intersection point. We give algorithms for each case to find the Frenet vectors (t, n, b(1), b(2)) and the curvatures (k(1), k(2), k(3)) of the non-transversal intersection curve. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free