Timelike tangent developable surfaces and Bonnet surfaces

This thesis consists of five chapters. The first chapter is devoted to the introduction. In the second chapter, the concepts of the angle and vector, basic definitions and necessary theorems in two and three dimensional Minkowski spaces are introduced. Third chapter is arranged as two subsections. Timelike surfaces and timelike Bonnet surfaces are summarized in these two subsections of the third chapter. A criterion is given for a timelike surface to be a Bonnet surface.The fourth chapter is the original part of this study and it is organized as two subsections. In the first part of the fourth chapter, a necessary and sufficient condition for a timelike tangent developable surface to be a timelike Bonnet surface is obtained under the condition of the curvature and torsion of the base curve of the timelike developable surface being non constant. In the second part, the curvature and torsion of the base curve of a timelike developable surface are considered as constant that is the base curve is considered as circular helix and the non-trivial isometry that preserves the mean curvature is obtained for a timelike developable surface which is a flat helicodial surface.In fifth chapter of this thesis, a brief summary of the study is given and a suggestion is proposed for new investigations.