Some Characterizations of Focal Surfaces of A Tubular Surface in E^3

Abstract

Here, we focus on focal surfaces of a tubular surface in Euclidean 3-space E^3: Firstly, we give the tubular surfaces with respect to Frenet and Darboux frames. Then, we define focal surfaces of these tubular surfaces. We get some results for these types of surfaces to become flat and we show that there is no minimal focal surface of a tubular surface in E^3. We give some examples for these type surfaces. Further, we show that u-parameter curves cannot be asymptotic curves and we obtain some results about v-parameter curves of the focal surface M^*.