Properties of twisted surfaces

The aim of this thesis is to reveal the problem of what kind of parametrization of twisted surfaces in 3-dimensional isotropic space and to give definitions, theorems and examples in the direction of solution of the problem. In addition, it was aimed to bring a different perspective to the concept of twisted surface by using Involüt-Evolüt and Bertrand curve pairs while forming the twisted surfaces in Euclidean space. The first chapter of this thesis, which consists of seven chapters, is divided into the introduction part. In the second part, the basic concepts and definitions which are necessary in the advanced chapters are given. In the third and fourth chapters, theorems and examples related to the curvatures of the twisted surfaces in 3-dimensional Euclidean space and 3-dimensional Minkowski space, respectively, have been examined. In the fifth chapter, characterizations of twisted surfaces and curvature calculations are discussed in 3-dimensional Isotropic space. In the sixth chapter, the curvature calculations, theorems and examples related to the twisted surface created by the Involute curve in 3-dimensional Euclidean space are given. Finally, in the seventh chapter, twisted surfaces formed by the curve of a Bertrand pair of a curve in 3-dimensional Euclidean space are discussed.