On the 5-axis motion of cutter and swept surfaces in minkowski space

This thesis study comprises seven sections. The introduction is placed in the first section of the study. Some definitions and theorems of the geometry of the curves and surfaces are given in the second section of the study. In 3-dimensional Euclidean and Minkowski space, distinct characterizations of the quasi-canal and quasi-tubular surfaces obtained through the quasi orthonormal frame are defined in the third section of the study. Then, some curvatures belonging to these surfaces are computed. In 3-dimensional Euclidean and Minkowski space, the concept of 5-axis motion of the quasi-canal and quasi-tubular surfaces obtained through the quasi orthonormal frame is investigated in the fourth section of the study. Later, a geometry of the specially designated cutter and swept quasi-canal and quasi-tubular surfaces are studied. In 3-dimensional Minkowski space, some applications of the 5-axis motion of the cutter and swept quasi-canal and quasi-tubular surfaces are given in the fifth section of the study. In 3-dimensional Euclidean and Minkowski space, inextensible Heisenberg ferromagnetic flows and quasi magnetic surfaces are defined for the most general form of 5-axis cutter and swept motion with the help of quasi orthonormal frame structure. The conclusion part is placed in the seventh section of the study.