Melek Masal

A Note on Inextensible Flows of Curves on Oriented Surface

OnderGokmenYildizDepartment of Mathematics,Faculty of Arts and Sciences,Bilecik Seyh EdebaliUniversity,Bilecik/TURKEYogokmen.yildiz@bilecik.edu.trSoleyErsoyDepartment of Mathematics,Faculty of Arts and Sciences,Sakarya University,Sakarya/TURKEYsersoy@sakarya.edu.trMelek MasalDepartment of MathematicsTeaching,Faculty of Education,Sakarya University,Sakarya/TURKEYmmasal@sakarya.edu.trABSTRACTIn this paper, we investigate a general formulation for inextensible flows of curves onan oriented surface in R

3-Boyutlu öklid uzayında bertrand eğriler ve bishop çatısı

Bu calismada 1975 yilinda L. R. Bishop tarafindan tanimlanan Bishop catisina ait egrilikliklerin geometrik anlamlari verildi. Daha sonra 1850 yilinda Bertrand’in tanimladigi Bertrand egri ciftlerinin Bishop vektorleri arasindaki bagintilar elde edildi. Ayrica bu Bertrand egri ciftlerinin paralel egri olmasi durumunda bazi ilginc sonuclar elde edildi.In this paper, the geometric meanings of the curvatures belong to Bishop frame, which was defined by L.R. Bishop in 1975, has been given. Afterwards, the relations between the Bishop vectors of Bertrand curve couple, which Bertrand defined in 1850, has been obtained. Furthermore, some interesting results have been found when these curves become parallel curves.

Generalized parallel p i -equidistant ruled surfaces

In this paper, parallel p i -equidistant ruled surfaces in 3-dimensional Euclidean space E 3 , [6], were generalized to n -dimensional Euclidean space E n . Then mean curvatures, Lipschitz–Killing curvatures, Gauss curvatures, scalar normal curvatures, Riemannian curvatures, Ricci curvatures, scalar curvatures of ( m + 1)-dimensional parallel p i -equidistant ruled surfaces were calculated and some relations between these curvatures were found. Also, examples related to the parallel p 3 -equidistant ruled surfaces in the E 3 are given.