Cilt:69 Sayı:01 (2020)

Permanent URI for this collection

https://dspace.ankara.edu.tr/handle/20.500.12575/75966

Browse

Browsing Cilt:69 Sayı:01 (2020) by Author "Abdel-Baky, Rashad"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    The relatively osculating developable surfaces of a surface along a direction curve
    (Ankara Üniversitesi Fen Fakültesi, 2020-06-30) Ünlütürk, Yasin; Abdel-Baky, Rashad; Other; Other
    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.
  • No Thumbnail Available
    Item
    W--line congruences
    (Ankara Üniversitesi Fen Fakültesi, 2020-06-30) Taş, Ferhat; Abdel-Baky, Rashad; Other; Other
    By utilizing the Darboux frames, along with a regular surface whose parametric curves are lines of curvature, we analyzed the normal line congruence which preserves the asymptotic curves between its focal surfaces. This allows deriving systems of partial differential equations through which the problem of determining the director surface and the corresponding normal line congruence could be solved. Moreover, a necessary and sufficient condition that the focal surfaces of the normal line congruence are degenerates into curves is derived. As a result, the middle focal surface of the normal line congruence is presented as a new surface interrogation tool.