On the characterications of curves which spherical indicatrices are conics

This thesis is written about the sphere geometry which is widely used today in mathematics. More precisely, it concerns the spherical curves, which are a field of study within the sphere geometry. This work is based on spherical conics. In addition, "T-conic", "B-conic" and "Nconic" curve families are defined, and "T-conic" and "B-conic" curves belong to the same curve family. From these results, the characterizations of the "T-conic" and "N-conic" curve families are obtained and in the result of these characterizations, the general helices belong to the "T-conic" curve family and the slant helices belong to the "N-conic" curve family. Moreover, various parametric equations related to "T-conic" curve families are given, which are explained by equations covering general helixes. Finally, various examples of these "T-conic" curve families are given in figures.