On the constant angle surface

The thesis consists of four parts. The first part is the entry of the thesis. In the second part, terms definitions and theorems which are necessary for Öklid space and Lorentz space are given. In the third part, constant angle surfaces and curves are studied in Euclidean 3-space. Special developable surfaces and some conical surfaces are examined from the point of view the constant angle property. Also, some characterization are given for a curve lying on a surface for which the unit normal makes a constant angle with a fixed direction. In the fourth part, constant angle surfaces and curves are handled in Lorentzian 3-space. Firstly, some characterizations are given for a curve lying on spacelike fixed direction timelike constant angle surface, and then some characterizations are given for a curve lying on spacelike fixed direction spacelike constant angle surface.