- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 69 Issue: 1
- The relatively osculating developable surfaces of a surface along a direction curve
The relatively osculating developable surfaces of a surface along a direction curve
Authors : Yasin Ünlütürk, Rashad Abdel-baky
Pages : 511-527
Doi:10.31801/cfsuasmas.527231
View : 8 | Download : 4
Publication Date : 2020-06-30
Article Type : Research
Abstract :We construct a developable surface tangent to a surface along a curve on the surface. We call this surface as relatively osculating developable surface. We choose the curve as the tangent normal direction curve on which the new surface is formed in the Euclidean 3-space. We obtain some results about the existence and uniqueness, and the singularities of such developable surfaces. We also give two invariants of curves on a surface which characterize these singularities. We present two results for special curves such as asymptotic line and line of curvature which are rulings of the relatively osculating surface.Keywords : Relatively osculating developable surfaces, Curves on surfaces, Ruled surfaces, Direction curve, Singularities