Smarandache Curves of Spacelike Anti-Salkowski Curve with a Timelike Principal Normal According to Frenet Frame

Year 2020, Volume: 13 Issue: 2, 404 - 416, 31.08.2020

Süleyman Şenyurt Kemal Eren

https://doi.org/10.18185/erzifbed.621344

Cited By: 1

Abstract

In this paper, we investigate the regular Smarandache curves obtained from the Frenet vectors of spacelike anti-Salkowski curve with a timelike principal normal. Firstly, we define Smarandache curves depending upon the anti-Salkowski curve. Later, the curvature and the torsion Frenet vectors of Smarandache curves are calculated. Finally, the Frenet apparatuses of the obtained Smarandache curves are expressed as Frenet vectors of the spacelike anti-Salkowski curve. We draw graphic of the obtained Smarandache curves and some related results are given.

Keywords

Minkowski space, spacelike anti-Salkowski curve, Mathematics

Frenet Çatısına Göre Timelike Normalli Spacelike Anti-Salkowski Eğrisinden Elde Edilen Smarandache Eğrileri

Abstract

Bu çalışmada ilk
olarak timelike normalli spacelike anti-Salkowski eğrisinin Frenet
vektörlerinden elde edilen regüler Smarandache eğrileri tanımlandı. Daha sonra
her bir Smarandache eğrisinin Frenet vektörleri, eğrilik ve torsiyonu
hesaplandı. Son olarak elde edilen eğrilerin Frenet elemanları spacelike
Salkowski eğrisinin Frenet elemanları cinsinden yazılarak grafikleri çizildi.Bu çalışmada ilk olarak timelike normalli spacelike anti-Salkowski eğrisinin Frenet vektörlerinden elde edilen regüler Smarandache eğrileri tanımlandı. Daha sonra her bir Smarandache eğrisinin Frenet vektörleri, eğrilik ve torsiyonu hesaplandı. Son olarak elde edilen eğrilerin Frenet elemanları spacelike Salkowski eğrisinin Frenet elemanları cinsinden yazılarak grafikleri çizildi.

Keywords

Minkowski uzayı, spacelike anti-Salkowski eğri, Matematik

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