Some characterizations of rectifying curves in the Euclidean space $E^4$

İLARSLAN, Kazım; NESOVIC, Emilija

Some characterizations of rectifying curves in the Euclidean space $E^4$

Kazım İLARSLAN, (Kırıkkale Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kırıkkale, Türkiye)

Emilija NESOVIC (Fac. of Science, Department,of Mathematics and Informatics, Radoja Domanovica 12 34000 Kragujevac, Serbia)

Turkish Journal of Mathematics

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Yıl: 2008 Cilt: 32 Sayı: 1 Sayfa Aralığı: 21 - 30 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Some characterizations of rectifying curves in the Euclidean space $E^4$

Öz:

In this paper, we define a rectifying curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement $N^{perp}$ of its principal normal vector field N. In particular, we study the rectifying curves in $Bbb{E}^4$ and characterize such curves in terms of their curvature functions.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Chen, B. Y.: When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110, 147-152 (2003).
[2] Chen, B. Y., Dillen, F.: Rectifying curves as centrodes and extremal curves, Bull. Inst. Math.Academia Sinica 33, No. 2, 77-90 (2005).
[3] Gluck, H.: Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73, 699-704, (1966).
[4] İlarslan, K., Nesovic, E., Petrovic-Torgasev, M.: Some characterizations of rectifying curves in the Minkowski 3-space, Novi Sad J. Math. Vol. 33, No. 2, 23-32, (2003).
[5] Millman, R. S., Parker, G. D.: Elements of differential geometry, Prentice-Hall, New Jersey,1977.
[6] Struik, D. J.: Differential geometry, second ed., Addison-Wesley, Reading, massachosetts, 1961.

APA	İLARSLAN K, NESOVIC E (2008). Some characterizations of rectifying curves in the Euclidean space $E^4$. , 21 - 30.
Chicago	İLARSLAN Kazım,NESOVIC Emilija Some characterizations of rectifying curves in the Euclidean space $E^4$. (2008): 21 - 30.
MLA	İLARSLAN Kazım,NESOVIC Emilija Some characterizations of rectifying curves in the Euclidean space $E^4$. , 2008, ss.21 - 30.
AMA	İLARSLAN K,NESOVIC E Some characterizations of rectifying curves in the Euclidean space $E^4$. . 2008; 21 - 30.
Vancouver	İLARSLAN K,NESOVIC E Some characterizations of rectifying curves in the Euclidean space $E^4$. . 2008; 21 - 30.
IEEE	İLARSLAN K,NESOVIC E "Some characterizations of rectifying curves in the Euclidean space $E^4$." , ss.21 - 30, 2008.
ISNAD	İLARSLAN, Kazım - NESOVIC, Emilija. "Some characterizations of rectifying curves in the Euclidean space $E^4$". (2008), 21-30.

APA	İLARSLAN K, NESOVIC E (2008). Some characterizations of rectifying curves in the Euclidean space $E^4$. Turkish Journal of Mathematics, 32(1), 21 - 30.
Chicago	İLARSLAN Kazım,NESOVIC Emilija Some characterizations of rectifying curves in the Euclidean space $E^4$. Turkish Journal of Mathematics 32, no.1 (2008): 21 - 30.
MLA	İLARSLAN Kazım,NESOVIC Emilija Some characterizations of rectifying curves in the Euclidean space $E^4$. Turkish Journal of Mathematics, vol.32, no.1, 2008, ss.21 - 30.
AMA	İLARSLAN K,NESOVIC E Some characterizations of rectifying curves in the Euclidean space $E^4$. Turkish Journal of Mathematics. 2008; 32(1): 21 - 30.
Vancouver	İLARSLAN K,NESOVIC E Some characterizations of rectifying curves in the Euclidean space $E^4$. Turkish Journal of Mathematics. 2008; 32(1): 21 - 30.
IEEE	İLARSLAN K,NESOVIC E "Some characterizations of rectifying curves in the Euclidean space $E^4$." Turkish Journal of Mathematics, 32, ss.21 - 30, 2008.
ISNAD	İLARSLAN, Kazım - NESOVIC, Emilija. "Some characterizations of rectifying curves in the Euclidean space $E^4$". Turkish Journal of Mathematics 32/1 (2008), 21-30.