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In this paper, the general formulation for inextensible flows of curves onoriented surface in $\mathbb{R}^3 $ is investigated. The necessary andsufficient conditions for inextensible curve flow lying an oriented surface areexpressed as a partial differential equation involving the geodesic curvatureand the geodesic torsion. Moreover, some special cases of inextensible curveson oriented surface are given.

A Note on Inextensible Flows of Curves on Oriented Surface