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

Aléssio, Osmar; Düldül, Mustafa; Düldül, Bahar Uyar; Badr, Sayed Abdel-Naeim; Abdel-All, Nassar H.

doi:10.1016/j.cagd.2014.09.003

Cited by 9 publications

(10 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(4) If the above conics overlap, then p is a higher-order contact point. (19) vanishes for any values of x ′ , y ′ and z ′ , i.e. p is a higher order contact point.…”

Section: Unit Tangent Vectormentioning

confidence: 96%

“…The number of the real intersection points of the above conic pairs yields the following cases as in [19]:…”

Section: Unit Tangent Vectormentioning

confidence: 99%

“…Recently, we study the non-transversal intersection of parametric-parametric-parametric (PPP) hypersurfaces [19] and the non-transversal intersection of implicit-implicit-parametric (IIP), implicit-parametric-parametric (IPP) hypersurfaces [20] in E 4 (we review the previous studies given for intersection problems in these publications).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Aléssio

Düldül

et al. 2016

Journal of Computational and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

a b s t r a c tThe 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 nontransversal 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.

show abstract

“…(4) If the above conics overlap, then p is a higher-order contact point. (19) vanishes for any values of x ′ , y ′ and z ′ , i.e. p is a higher order contact point.…”

Section: Unit Tangent Vectormentioning

confidence: 96%

“…The number of the real intersection points of the above conic pairs yields the following cases as in [19]:…”

Section: Unit Tangent Vectormentioning

confidence: 99%

See 1 more Smart Citation

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

Aléssio

Düldül

et al. 2016

Journal of Computational and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…A general reference including many topics in semi-Riemannian geometry is the classical book [19]. Differential geometry of the intersection curves in R 3 and R 4 can be found in [14,26,23,1,15,7,2,4,8,5,3].…”

Section: Introductionmentioning

confidence: 99%

“…Some results on differential geometry of the intersection curves for the transversal intersections in Minkowski 3-space R 3 1 , and Minkowski 4-space R 4 1 , can be found in [6,22,16] and [13] respectively. Aléssio and Guadalupe [6] studied the transversal intersection curve of two parametric spacelike surfaces in R 3 1 considering parametric-parametric intersection problem.…”

Section: Introductionmentioning

confidence: 99%