Normal Surfaces along a Curve on a Surface in Euclidean 3-Space

Curves on surfaces and their frames play an important role in differential geometry and in many branches of science such as mechanics and physics. So, we are interested in studying one of these surfaces along a curve lying on a surface. In this paper, we define a surface normal to a surface along a curve lying on a surface in Euclidean 3-space E3. Then, we analyze the necessary and sufficient conditions for that surface to be a ruled surface. Finally, we illustrate the convenience and efficiency of this approach with some representative examples.