8-Boyutlu Oktoniyon Uzayında Reel Oktoniyonları Kullanarak Oktoniyonik Rektifiyan, Oskülatör ve Normal Eğrilerin Özelliklerinin Belirlenmesi

Yıl 2018, Cilt: 11 Sayı: 1, 31 - 46, 24.04.2018

Özcan Bektaş Salim Yüce

Öz

Bu çalışmada, 8-boyutlu oktoniyon uzayda, reel oktoniyonlarla, oktoniyonik rektifiyan, oskülatör ve normal

eğrilerin özelliklerinin nasıl belirlenebileceği konusu üzerine odaklanılmıştır. Öncelikle, oktoniyonlar cebirleri

ve 8-boyutlu oktoniyon uzayında oktoniyonik eğriler hakkında bazı bilgiler verilmiştir. Daha sonra 8-boyutlu

oktoniyon uzayda oktoniyonik rektifiyan, oskülatör ve normal eğrileri tanımlanmıştır. Son olarak, oktoniyonik

rektifiyan, oskülatör ve normal eğrilerin bazı karakterizasyonları elde edilmiştir.

Anahtar Kelimeler

Oktoniyonik rektifiyan eğri, Oktoniyonik oskülatör eğri, Oktoniyonik normal eğri, Oktoniyon uzay

Determination of Properties of Octonionic Rectifying, Osculating and Normal Curves Using Real Octonions in 8-Dimensional Octonion Space

Öz

In this study, we focus on the issue of how to determine properties of octonionic rectifying, osculating and

normal curves by means of real octonions in 8-dimensional octonion space. Firstly, we give some informations

about octonion algebras, and octonionic curves in 8-dimensional octonion space. After that, we define

octonionic rectifying, osculating and normal curves in 8-dimensional octonion space. Finally, we obtain some

characterizations of the octonionic rectifying, osculating and normal curves.

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octonionic rectifying, osculating and normal curves in 8-dimensional octonion space. Finally, we obtain some

characterizations of the octonionic rectifying, osculating and normal curves.

Anahtar Kelimeler

Octonionic rectifying curve, Octonionic osculating curve, Octonionic normal curve, Octonion space

Kaynakça

• Baez, JC. 2001. The Octonions, Bull Am Math Soc, 39, 145-205.
• Bektaş, Ö., Gürses (Bayrak), N., Yüce, S. 2016. Quaternionic Osculating Curves in Euclidean and Semi-Euclidean Space, Journal of Dynamical Systems and Geometric Theories, 14(1), 65-84.
• Bektaş, Ö., Yüce, S. 2014. Real Variable Serret Frenet Formulae of an Octonion Valued Function (Octonionic Curves). Colloquium on Combinatorics, 7-8 November 2014, Ilmenau
• Bharathi, K., Nagaraj, M. 1987. Quaternion Valued Function of a Real Variable Serret-Frenet Formulae. Indian J Pure Appl Math, 18, 07-511.
• Cambie, S., Goemans, W., Van Den Bussche, I. 2016. Rectifying Curves in the n-Dimensional Euclidean Space, Turk J Math, 40, 210-223.
• Chen, BY. 2003. When Does the Position Vector of a Space Curve Always Lie in its Rectifying Plane?, Am Math Mon, 110, 147-152.
• Chen, BY., Dillen, F. 2005. Rectifying Curves as Centrodes and Extremal Curves. Bull Inst Math Acad Sin, 33, 77-90.
• Dray, T., Manogue, C., (2015). The Geometry of Octonions, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
• Hamilton, WR. (1969). Elements of Quaternions, Chelsea Publications, New York, USA.
• İlarslan, K., Nesovic, E. Petrovic-Torgasev, M. 2003. Some Characterizations of Rectifying Curves in the Minkowski 3-Space, Novi Sad J Math, 33, 23-32.
• İlarslan, K., Nesovic, E. 2007. On Rectifying Curves as Centrodes and Extremal Curves in Minkowski 3-Space, Novi Sad J Math, 37, 53-64.
• İlarslan, K., Nesovic, E. 2008a. Some Characterizations of Rectifying Curves in the Euclidean space E^4, Turk J Math, 32, 21-30.
• İlarslan, K., Nesovic, E. 2008b. Some Characterizations of Osculating Curves in the Euclidean Spaces, Demonstratio Mathematica, XLI, 4, 931-939.
• Güngör, MA., Tosun, M. 2011. Some Characterizations of Quaternionic Rectifying Curves, Differential Geometry, Dynamical Systems, 13, 102-113.
• Ward, JP. (1997). Quaternions and Cayley Numbers Algebra and Applications, Kluwer Academic Publishers, London.
• Yıldız, Ö.G., Özkaldı Karakuş, S. 2013. On the Quaternionic Normal Curves in the Euclidean Space, 2nd International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2013), 26-29Ağustos 2013, Bosna Hersek.
• Yıldız, Ö.G., Özkaldı Karakuş, S. 2016. On the Quaternionic Normal Curves in the Semi Euclidean Space , International Journal of Mathematical Combinatoric, 3, 68-76.