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

BADR S. A., ABDEL-ALL N. H., ALESSIO O., DÜLDÜL M., Duldul B. U.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.288, ss.81-98, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 288
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1016/j.cam.2015.03.054
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.81-98
  • Anahtar Kelimeler: Implicit-implicit-parametric intersection, Implicit-parametric-parametric intersection, Non-transversal intersection, Curvatures, DIFFERENTIAL GEOMETRY
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.