On the evolute offsets of ruled surfaces in Minkowski 3-space

Yoon, Dae Won

On the evolute offsets of ruled surfaces in Minkowski 3-space

Dae Won YOON (Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, Republic of Korea)

Turkish Journal of Mathematics

1 0

Yıl: 2016 Cilt: 40 Sayı: 3 Sayfa Aralığı: 594 - 604 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

On the evolute offsets of ruled surfaces in Minkowski 3-space

Öz:

In this paper, we classify evolute offsets of a ruled surface in Minkowski 3-space L 3 with constant Gaussian curvature and mean curvature. As a result, we investigate linear Weingarten evolute offsets of a ruled surface in L 3 .

Anahtar Kelime:

Konular: Matematik

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

[1] As E, Sario˘glugil A. On the Bishop curvatures of involute-evolute curve couple in E 3 . Intern J Phys Sci 2014; 9: 140-145.
[2] Babaarslan M, Yayli Y. Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space. Proc Nat Acad Sci India Sect A 2014;84: 535-540.
[3] Babaarslan M, Yayli Y. On space-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space. arXiv:1112.1504v6 2014.
[4] Choi JH, Kang TH, Kim, YH. Bertrand curves in 3-dimensional space forms. Applied Math Computation 2012;219: 1040-1046.
[5] Farouki RT. The approximation of non-degenerate offset surfaces. Comput Aided Geom Design 1986;3: 15-43.
[6] Kasap E, Kuruo˘glu N. The Bertrand offsets of ruled surfaces in R 3 1 . Acta Math Vietnam 2006; 31: 39-48.
[7] Kasap E, Y¨uce S, Kuruo˘glu N. The involute-evolute offsets of ruled surfaces. Iranian J Sci Tech Transaction A 2009; 33: 195-201.
[8] K¨ulah¸cı M, Erg¨ut M. Bertrand curves of AW(k)-type in Lorentzian space. Nonlinear Analysis 2009; 70: 1725-1731.
[9] Liu H, Wang F. Mannheim partner curves in 3-space. J Geom 2008; 88: 120-126.
[10] Matsuda H, Yorozu S. On generalized Mannheim curves in Euclidean 4-space. Nihonkai Math J 2009; 20: 33-56.
[11] Onder M. Some characterizations of Bertrand offsets of timelike ruled surfaces. J Adv Res Dyn Control Syst 2011; ¨ 3: 21-35.
[12] Onder M, U˘gurlu HH. Dual Darboux frame of a timelike ruled surface and Darboux approach to Mannheim offsets ¨ of timelike ruled surfaces. Proc Nat Acad Sci India Sect A 2013; 83: 163-169.
[13] Onder M, U˘gurlu HH. Frenet frames and invariants of timelike ruled surfaces. Ain Shams Eng J 2013; 4: 507-513. ¨
[14] Orbay K, Kasap E, Aydemir I. Mannheim offsets of ruled surfaces. Math Problems Engineering 2009; Article ID 160917, 9 pages.
[15] Ravani B, Ku TS. Bertrand offsets of ruled and developable surfaces. Comput Aided Geom Design 1991; 23: 145-152.
[16] Walrave J. Curves and surfaces in Minkowski space. PhD, K. U. Leuven, Fac. of Science, Leuven, Belgium, 1995.
[17] Yılmaz MY, Bektas M. General properties of Bertrand curves in Riemann-Otsuki space. Nonlinear Analysis 2008; 67: 3225-3231.
[18] Yoon DW. Mannheim curves in an n-dimensional Lorentz manifold. Intern J Pure Appl Math 2014; 96: 165-174.

APA	Yoon D (2016). On the evolute offsets of ruled surfaces in Minkowski 3-space. , 594 - 604.
Chicago	Yoon Dae Won On the evolute offsets of ruled surfaces in Minkowski 3-space. (2016): 594 - 604.
MLA	Yoon Dae Won On the evolute offsets of ruled surfaces in Minkowski 3-space. , 2016, ss.594 - 604.
AMA	Yoon D On the evolute offsets of ruled surfaces in Minkowski 3-space. . 2016; 594 - 604.
Vancouver	Yoon D On the evolute offsets of ruled surfaces in Minkowski 3-space. . 2016; 594 - 604.
IEEE	Yoon D "On the evolute offsets of ruled surfaces in Minkowski 3-space." , ss.594 - 604, 2016.
ISNAD	Yoon, Dae Won. "On the evolute offsets of ruled surfaces in Minkowski 3-space". (2016), 594-604.

APA	Yoon D (2016). On the evolute offsets of ruled surfaces in Minkowski 3-space. Turkish Journal of Mathematics, 40(3), 594 - 604.
Chicago	Yoon Dae Won On the evolute offsets of ruled surfaces in Minkowski 3-space. Turkish Journal of Mathematics 40, no.3 (2016): 594 - 604.
MLA	Yoon Dae Won On the evolute offsets of ruled surfaces in Minkowski 3-space. Turkish Journal of Mathematics, vol.40, no.3, 2016, ss.594 - 604.
AMA	Yoon D On the evolute offsets of ruled surfaces in Minkowski 3-space. Turkish Journal of Mathematics. 2016; 40(3): 594 - 604.
Vancouver	Yoon D On the evolute offsets of ruled surfaces in Minkowski 3-space. Turkish Journal of Mathematics. 2016; 40(3): 594 - 604.
IEEE	Yoon D "On the evolute offsets of ruled surfaces in Minkowski 3-space." Turkish Journal of Mathematics, 40, ss.594 - 604, 2016.
ISNAD	Yoon, Dae Won. "On the evolute offsets of ruled surfaces in Minkowski 3-space". Turkish Journal of Mathematics 40/3 (2016), 594-604.