A note on inextensible flows of curves on oriented surface

Onder Gokmen Yildiz; Soley Ersoy; Melek Masal

doi:10.4067/S0719-06462014000300002

Authors

Onder Gokmen Yildiz Department of Mathematics, Faculty of Arts and Sciences, Bilecik Seyh Edebali University, Bilecik, Turkey.
Soley Ersoy Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya, Turkey.
Melek Masal Department of Mathematics Teaching, Faculty of Education, Sakarya University, Sakarya, Turkey.

DOI:

https://doi.org/10.4067/S0719-06462014000300002

Keywords:

Curvature flows, inextensible, oriented surface

Abstract

In this paper, we investigate a general formulation for inextensible flows of curves on an oriented surface in R³. We obtain necessary and sufficient conditions as partial differential equations involving the geodesic curvature and the geodesic torsion for inextensible curve flow lying on an oriented surface. Moreover, some special cases of inextensible curves on oriented surface are given.