Offset ruled surfaces with density

This thesis consists of four chapters. The first chapter is devoted to the introduction part. In the second chapter, curves theory, characteristics of surfaces and the basic definitions of ruled surface and necessary theorems in three-dimensional Euclidean surface are introduced. The calculation of mean and Gaussian curvature of surfaces with density are given in the third chapter. In addition, the characteristics of surfaces with density are given. The fourth chapter generates the original part of this study and it is organized as two subsections. In the first subsection of this chapter, the relations between the mean curvature and Gaussian curvature of offset ruled surfaces with density are given. In the second subsection, the relationships between the mean curvature of the ruled surfaces with e^(-x^2-y^2) density, and the mean curvature with density is given instead of the e^z density. In addition, the relations between the mean curvature of the ruled offset surface with density and the mean curvature with density are given. The same relations are also given between Gaussian curvature and density Gaussian curvature.