New frames and new offsets for ruled surfaces

In this thesis, a new frame and new offsets for ruled surfaces, which are the important topics of differential geometry, have been defined. The thesis consists of four sections. In the first section as given introduction, a literature information about the importance of ruled surfaces and definitions of well-known types of offset surfaces have been given. In the Second Section, it has been mentioned the theory of ruled surfaces in the 3-dimensional Euclidean space E^3. The Frenet frame defined along the striction line of a ruled surface has been reminded. Moreover, definitions and characterizations of Bertrand and Mannheim offsets of ruled surfaces and of slant ruled surfaces according to Frenet frame have been given. In the third section, a new orthonormal frame along the striction curve of a ruled surface has been defined. This frame has been called alternative frame and derivative formulas for this new frame have been obtained. In the fourth section, four new offsets of ruled surfaces have been defined. The equations characterizing these new offsets have been given and some conditions for offset surfaces to be developable have been obtained. Some results giving the relationships between some of these new offsets and slant ruled surfaces have been obtained. Furthermore, the characterizations for Bertrand offsets have been given according to alternative frame. The original part of this thesis are the third and fourth sections.