Translation surfaces according to bishop frame in minkowski 3-space

In this study, translation surfaces generated by spatial curves which are not planar are investigated according to Bishop frame in Minkowski 3-space. First fundamental forms, second fundamental forms, Gaussian curvatures and mean curvatures of the obtained surfaces are calculated. This thesis consists of three sections. In the first section, literature information of about studies on translation surfaces according to Frenet and Darboux frame in Euclidean spaces and Minkowski 3-space are stated. Moreover, some studies in Euclidean spaces are summarized on translation surfaces according to Bishop and Darboux frames which are alternatives to Frenet frame. In the second section, basic concepts on the theory of curves and surfaces in Euclidean 3-space are stated. Derivative formulas according to Frenet and Bishop frames and relations between these frames are given. First and second funfamental forms and surface curvatures are summarized which are necessary to investigate a surface. Furthermore, basic concepts of Minkowski 3-space and theory of curves and surfaces in this space are given by details. In the third section, first fundamental forms, second fundamental forms, Gaussian curvatures and mean curvatures of translation surfaces according to Bishop frame are calculated in Minkowski 3-space. During this calculation, spacelike and timelike translation surfaces are handled separately for different cases. For spacelike translation surfaces, first fundamental forms, second fundamental forms, Gaussian curvatures, and mean curvatures are calculated in four different cases. For timelike translation surfaces, first fundamental forms, second fundamental forms, Gaussian curvatures and mean curvatures are calculated in nine different cases with respect to the curve on the surface is spacelike or timelike.