Ruled surfaces of Weingarten type in Euclidean 3-space and Lorentzian 3-space

This study prepared as master thesis consists of four chapters. The first chapter is organized as an introduction and some fundamental information about the development of Weingarten ruled surfaces has been presented. The second chapter is divided to some fundamental concepts related to curves and surfaces in 3-dimensional Euclidean and Lorentzian space. In the third chapter, Weingarten ruled surfaces in the 3-dimensional Euclidean space have been investigated. The theorems and results including the necessary and sufficent conditions for a ruled surface to be Weingarten surface are given. In the fourth chapter, the ruled Weingarten surfaces in 3-dimensional Lorentzian space are considered. The geometric conclusions with respect to the causal characteristics of the directed vector X and base curve α in E_1^3 are presented.