Involute-evolute offset ruled surfaces whose striction curves are involute-evolute curve pairs

This thesis consists of five chapters. In the first chapter, general information about curve pairs and offset ruled surfaces in 3-dimensional Euclidean space is given and the studies on these subjects in the literature are summarized. In the second chapter, the differential geometric properties of curves, surfaces and ruled surfaces used in the thesis are introduced and definitions and theorems related to these subjects are given. In the third chapter, some differential geometric properties of a ruled surface whose base curve is taken as the striction curve and whose directrix vector is the linear combination of the Frenet vectors of the striction curve are given. In the fourth chapter, which is the original part of the thesis, involute-evolute offset ruled surfaces whose striction curves are involute-evolute curve pair are examined for four different cases. In each case, it is determined under which conditions the ruled surfaces form the involute-evolute offset relationship. The first and second fundamental coefficients, Gaussian and mean curvatures of offset ruled surfaces are found, and the developability and minimality of these ruled surfaces are determined. In addition, normal curvatures, geodesic curvatures and geodesic torsions of striction curves of offset ruled surfaces are found, and it has been examined whether these curves are asymptotic curves, geodesic curves or curvature lines. An example is given for each of the four different cases in the study. In the fifth chapter, the results obtained in the thesis, comparisons of these results with existing studies in the literature and suggestions for new studies have been given.