The geometry of curves and surfaces in minkowski 3-space

In the introduction chapter of this thesis consisting of four chapters, some generalevaluations have been done about the subject and some studies which are main into thissubject have been presented.In the second chapter, some fundamental notions which will be used in the laterchapters have been given.In the third chapter, firstly the general structures of the curves have been investigatedin E31 Minkowski 3-space, the Frenet equations have been obtained for different causalcharacters of curves and the curvature and torsion of the curves have been investigatedwith the aid of these equations. After, the planar curves with constant curvature havebeen handled in E31 . Furthermore, some characterizations about helices and Bertrandcurves have been given in this space. In this chapter, lastly, spacelike, timelike and nullnormal curves have been presented in E31.In the fourth chapter, firstly the notions of spacelike and timelike surfaces have beenintroduced and after the mean curvature and Gaussian curvature have been locally denotedfor these surfaces. Moreover, the umbilical surfaces of E31 have been characterized. After,the rotation surfaces have been generally introduced in E31 and some characterizationsabout these surfaces have been given. And lastly, the general structures of ruled surfacesand some characterizations for timelike ruled surfaces have been given.