Geometries and characterizations of slant ruled surfaces in minkowski 3-space

This thesis is basically a study on the geometry of curves and surfaces in Minkowski 3-space. First, basic information is given in the Euclidean and Minkowski 3-spaces. The definitions of helix and slant helix are presented and the concept of slant is stated. Later, basic notions regarding ruled surfaces are given and slant ruled surfaces are introduced which are formed by uniting the concept of slant with ruled surfaces. Slant ruled surfaces are defined as three different types called q-slant, h-slant and a-slant in Minkowski 3-space as they are defined in the Euclidean 3-space. However, the vectors, curves and surfaces could be from spacelike, timelike and lightlike character in the Minkowski 3-space. In this thesis, the geometry of spacelike and timelike slant ruled surfaces are investigated. Spacelike and timelike Darboux slant ruled surfaces are defined and theorems about such surfaces are given. Differential equation characterizations for spacelike and timelike slant ruled surfaces and for the slant ruled surfaces which are drawn by the Frenet vectors of such surfaces are deducted. Finally, spacelike and timelike q-slant and h-slant developable ruled surfaces and their position vectors are investigated.