Characterization of quaternionic some surfaces in minkowski 3-space

This thesis consist of seven chapters. The first chapter is an introduction which information about studies of curves in Minkowski space, surfaces, sea shell surface and bisector surface. In the second chapter; fundemental definitions and theorems used in the study are given. In the third section includes material and method section. Fourth, fifyh and sixth sections are the original part of the study. In the fourth chapter; helical spiral in Minkowski space is defined firstly a new surface in Minkowski space called sea shell surface is defined which consider this curve as central curve in the case of this helical spiral timelike or spacelike. Then, quaternionic sea shell surface is created from different characterization of this surface. Finally, Gaussian and mean curvatures is obtained by quaternionic method different from differential geometry. In the fifth chapter; spatial split quaternionic curve-curve bisector surface is defined. Furthermore, degerenate case of this surface is investigated. Then, bisectors of split quaternionic curves is created from a point and degenerate case of this surface is obtained. Finally, Gaussian and mean curvatures of these two spaces are obtained by quaternionic operations different from classical differential geometry. In the sixth chapter, some application concerned about quaternionic sea shell surfaces and quaternionic bisector surfaces are given. The seventh chapter is a devoted to the conclusion.