Spherical indicatrix curves in multiplicative space

This thesis is composed of five chapters. The first chapter presents the introduction and the general framework of the study. The second chapter includes the fundamental concepts that will be used in the subsequent sections. In this part, the basic definitions and theorems related to the theory of curves in three-dimensional Euclidean space are provided. In the third chapter, the concept of multiplicative space is introduced. The basic operations that will be used in the following sections are defined, and the fundamental definitions and theorems concerning the theory of curves in the multiplicative space are discussed. The fourth chapter investigates the multiplicative spherical indicatrix curves in the multiplicative space. Considering the multiplicative Frenet frame of a curve in three-dimensional multiplicative Euclidean space, there exist three multiplicative indicatrix curves: the multiplicative tangent indicatrix, the multiplicative principal normal indicatrix, and the multiplicative binormal indicatrix. For each of these curves, their corresponding multiplicative Frenet frames, curvatures, and torsions are computed. Moreover, the relationships between these indicatrix curves are examined through the study of multiplicative Bertrand and involute–evolute curve pairs. Examples and figures supporting the theoretical results obtained in this study are also provided. Finally, the fifth chapter presents the conclusions of the study.