On the Quaternionic Focal Curves

Nurten (bayrak) Gürses; Özcan Bektaş; Salim Yüce

doi:10.19113/sdufbed.14005

On the Quaternionic Focal Curves

Öz

In this study, a brief summary about quaternions and quaternionic curves are firstly presented. Also, the definition of focal curve is given. The focal curve of a smooth curve consists of the centers of its osculating hypersphere. By using this definition and the quaternionic osculating hyperspheres of these curves, the quaternionic focal curves in the spaces $\Q$ and $\Q_\nu$ with index $\nu=\{1,2\}$ are discussed. Some relations about spatial semi-real quaternionic curves and semi-real quaternionic curves are examined by using focal curvatures and "scalar Frenet equations" between the focal curvatures. Then, the notions: such as vertex, flattenings, a symmetry point are defined for these curves. Moreover, the relation between the Frenet apparatus of a quaternionic curve and the Frenet apparatus of its quaternionic focal curve are presented.

Anahtar Kelimeler

Quaternions,Quaternionic curves; Osculating hypersphere; Focal curves; Semi-Euclidean space

Kaynakça

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Ayrıntılar

Birincil Dil

Türkçe

Konular

-

Bölüm

-

Yazarlar

Nurten (bayrak) Gürses

Özcan Bektaş

Salim Yüce

Yayımlanma Tarihi

13 Haziran 2017

Gönderilme Tarihi

18 Kasım 2016

Kabul Tarihi

-

Yayımlandığı Sayı

Yıl 2017 Cilt: 21 Sayı: 2

DOI

https://doi.org/10.19113/sdufbed.14005

IZ

https://izlik.org/JA74NY39NL

Kaynak Göster

RIS / Bibtex

APA

(bayrak) Gürses, N., Bektaş, Ö., & Yüce, S. (2017). On the Quaternionic Focal Curves. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(2), 357-366. https://doi.org/10.19113/sdufbed.14005

AMA

1.(bayrak) Gürses N, Bektaş Ö, Yüce S. On the Quaternionic Focal Curves. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2017;21(2):357-366. doi:10.19113/sdufbed.14005

Chicago

(bayrak) Gürses, Nurten, Özcan Bektaş, ve Salim Yüce. 2017. “On the Quaternionic Focal Curves”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 (2): 357-66. https://doi.org/10.19113/sdufbed.14005.

EndNote

(bayrak) Gürses N, Bektaş Ö, Yüce S (01 Ağustos 2017) On the Quaternionic Focal Curves. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 2 357–366.

IEEE

[1]N. (bayrak) Gürses, Ö. Bektaş, ve S. Yüce, “On the Quaternionic Focal Curves”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 21, sy 2, ss. 357–366, Ağu. 2017, doi: 10.19113/sdufbed.14005.

ISNAD

(bayrak) Gürses, Nurten - Bektaş, Özcan - Yüce, Salim. “On the Quaternionic Focal Curves”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21/2 (01 Ağustos 2017): 357-366. https://doi.org/10.19113/sdufbed.14005.

JAMA

1.(bayrak) Gürses N, Bektaş Ö, Yüce S. On the Quaternionic Focal Curves. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2017;21:357–366.

MLA

(bayrak) Gürses, Nurten, vd. “On the Quaternionic Focal Curves”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 21, sy 2, Ağustos 2017, ss. 357-66, doi:10.19113/sdufbed.14005.

Vancouver

1.Nurten (bayrak) Gürses, Özcan Bektaş, Salim Yüce. On the Quaternionic Focal Curves. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 01 Ağustos 2017;21(2):357-66. doi:10.19113/sdufbed.14005