Fen Bilimleri Enstitüsü
Matematik Anabilim Dalı
 

M.Sc. Tezi Görüntüleme

Student: Gönül Öztürk
Supervisor: Doç. Dr. Yasemin Sağıroğlu
Department: Matematik
Institution: Graduate School of Natural and Applied Sciences
University: Karadeniz Technical University Turkey
Title of the Thesis: k-Constant Eğriler
Level: M.Sc.
Acceptance Date: 20/6/2019
Number of Pages: 65
Registration Number: i3599
Summary:

      In this thesis, definitions of k-constant curves are given and Frenet frame, curvature

and torsion functions of these curves are calculated.

      In Chapter 1, forming the infrastructure of the study, 3-dimensional Euclidean

Space, Curves in the 3-dimensional Euclidean Space, Unit Speed Parametrization of

      Curves, Vector Fields in 3-dimensional Euclidean Space, Frenet Formulas in Unit Speed

Curves and Arbitrary Speed Curves are given.

      In Chapter 2, the definitions of k-constant tangent, k-constant normal and kconstant

binormal curves derived from a unit speed curve are given. Frenet frames,

      curvature and torsion functions of these curves are determined by using Frenet apparatus of

the unit speed curve. Finally, examples of k-constant curves of a unit-speed curve are given

      and their Frenet apparatus are calculated.

      Key Words: Curve, Frenet Frame, Curvature and Torsion Functions