VARIOUS CHARACTERIZATIONS FOR QUATERNIONIC MANNHEIM CURVES IN THREE-DIMENSIONAL EUCLIDEAN SPACE

Yıl 2021, Cilt: 4 Sayı: 1, 62 - 72, 31.01.2021

Aykut Has , Beyhan Yılmaz

https://doi.org/10.33773/jum.856869

Cited By: 2

https://izlik.org/JA38EC39FB

Öz

In this article, quaternionic curves in 3-dimensional Euclidean space have examined. Firstly, algebraic properties of quaternions and their basic definitions and theorems are given. Later, some characterizations of the quaternionic Mannheim curves in the 3-dimensional Euclidean space have obtained.

Anahtar Kelimeler

Real quaternions , Spatial quaternion , Quaternion Algebra , Mannheim partner curves

Kaynakça

• Referans1 J. P. Ward, Quaternions and Cayley Numbers, Kluwer Academic Publishers, Boston/London, (1997).
• Referans2 K. Bharathi and M. Nagaraj, Quaternion Valued Function of a Real Variable Serret-Frenet Formulae, Indian Journal of Pure and Applied Mathematics, 18 (6), 507--511, (1987).
• Referans3 A.Tuna, Serret Frenet formulae for Quaternionic Curves in Semi Euclidean Space, Master Thesis, Süleyman Demirel University, Graduate School of Natural and Applied Science, Isparta Turkey,(2002).
• Referans4 A. C. Çöken and A. Tuna, On the quaternionic inclined curves in the semi-Euclidean space E24 , Applied Mathematics and Computation, 155 (2), 373-- 389, (2004).
• Referans5 F. Kahraman, I. Gök, and H. H. Hacısalihoglu, On the quaternionic B2 slant helices in the semi- Euclidean space E24, Applied Mathematics and Computation, 218(11) , 6391--6400, (2012).
• Referans6 H. Liu and F. Wang, Mannheim partner curves in 3-space, J. Geom., 88, 120--126, (2008).
• Referans7 O. Z. Okuyucu, Characterizations of the quaternionic Mannheim curves in Euclidean space E4, International Journal of Mathematical Combinatorics, 2:44-53, (2013).
• Referans8 R. Blum, A remarkable class of Mannheim-curves, Canadian Mathematical Bulletin, 9:223-228, (1966).
• Referans9 J. W. Lee, No null-Helix Mannheim curves in the Minkowski Space , International Journal of Mathematics and Mathematical Sciences, Article ID 580537: 7 pages, doi.10.1155/2011/580537, (2011).
• Referans10 K. Orbay and E. Kasap, On Mannheim partner curves in E3, International Journal of Physical Sciences, 4 (5), 261-264, (2009).
• Referans11 H.B. Öztekin and M. Ergüt, Null Mannheim curves in the Minkowski 3-space, Turkish Journal of Mathematics, 35(1):107-114. International Journal of Physical Sciences, 4(5):261-264, (2011).
• Referans12 O.Z. Okuyucu, Characterizations of the quaternionic Mannheim curves in Euclidean space E4, International Journal of Mathematical Combinatorics, 2:44-53, (2013).
• Referans13 H. H. Hacısalioglu, Hareket Geometrisi ve Kuaterniyonlar Teorisi, University of Gazi Press, Ankara, (1983).
• Referans14 A. Mannheim, Paris C.R. 86 1254--1256, (1878).
• Referans15 H. H. Hacısalioglu, Diferansiyel Geometri , University of Ankara Press, Ankara, (1998).