3-boyutlu Öklid Uzayında q-çatılı Tzitzeica Eğrilerinin Karakterizasyonu

Year 2025, Volume: 29 Issue: 3, 688 - 693, 25.12.2025

Gamze Nur Şen , Gül Uğur Kaymanlı , Cumali Ekici

https://doi.org/10.19113/sdufenbed.1805264

Abstract

Bu çalışmada, q-çatısı kullanılarak 3 boyutlu Öklid uzayında Tzitzeica, küresel ve küresel Tzitzeica eğrileri analiz edilmiştir. Burulmasının, eğri üzerindeki herhangi bir noktada orijinden tanjant ve normal vektörler ile üretilen düzleme olan uzaklığın karesine oranı sıfırdan farklı sabit bir değere sahip olduğu bir Tzitzeica eğrisi vardır. 3-boyutlu Öklid uzayında Tzitzeica ve küresel eğrileri q-çatısı kullanılarak tanımlayıp ilgili teoremleri inceledikten sonra, küresel Tzitzeica eğrileriyle ilgili teoremler ispatlanmıştır.

Keywords

Eğrilikler , Küresel eğriler , Tzitzeika eğrileri

Characterization of Tzitzeica Curves by Using q-frame in Euclidean 3-space

Abstract

In this work, using q-frame Tzitzeica (T-curve), spherical (s-curve), and spherical Tzitzeica (sT-curve) curves are studied in three-dimensional Euclidean space. There is a T-curve when its torsion has a non-zero constant ratio to the square of the distance from the origin to the plane generated by tangent and normal vectors at any point on the curve. Using q-frame in 3-dimensional Euclidean space, after defining T-curve and s-curve and investigating related theorems, the theorems related to sT-curves are proved.

Keywords

Curvatures , Spherical curves , Tzitzeica curves

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