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

Citations of this article
Mendeley users who have this article in their library.


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.




Badr, S. A. N., Abdel-All, N. H., Aléssio, O., Düldül, M., & Uyar Düldül, B. (2015). Non-transversal intersection curves of hypersurfaces in Euclidean 4-space. Journal of Computational and Applied Mathematics, 288, 81–98.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free