Translation surfaces according to Bishop frame in Euclidean 3-space

Abstract

In this paper, by using non-planer space curves the translation surfaces are investigated according to Bishop frames in Euclidean 3-space. We have calculated the first and second fundamental quantities. We give the gaussian and mean curvatures of these surfaces according to the first and second Bishop curvatures in Euclidean 3-space. Also, using the Bishop curvatures of generating curves of translation surface, we give the necessary and sufficient conditions for generating curves to be geodesic and asymptotic curves on the surface.