Please wait a minute...
ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2006, Vol. 7 Issue (3 ): 8-    DOI: 10.1631/jzus.2006.A0326
    
On the Ruled surfaces in Minkowski 3-space R13
Öğrenmiş Alper Osman, Balgetir Handan, Ergüt Mahmut
Department of Mathematics, Faculty of Arts and Sciences, Fırat University, Elazığ, Turkey
Download:     PDF (0 KB)     
Export: BibTeX | EndNote (RIS)      

Abstract  Izumiya and Takeuchi (2003) obtained some characterizations for Ruled surfaces. Turgut and Hacısalihoğlu (1998) defined timelike Ruled surfaces and obtained some characterizations in timelike Ruled surfaces. Choi (1995) and Jung and Pak (1996) studied Ruled surfaces. This study uses the method in (Izumiya and Takeuchi, 2003) to investigate cylindrical helices and Bertrand curves as curves on timelike Ruled surfaces in Minkowski 3-space R13. We have studied singularities of the rectifying developable (surface) of a timelike curve. We observed that the rectifying developable along a timelike curve α is non-singular if and only if α is a cylindrical helice. In this case the rectifying developable is a cylindrical surface.

Key words： Timelike Ruled surfaces      Bertrand curve      Cylindrical helices     
Received: 20 September 2005     
CLC:  O211.4  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Öğrenmiş Alper Osman
Balgetir Handan
Ergüt Mahmut
Cite this article:

Öğrenmiş Alper Osman, Balgetir Handan, Ergüt Mahmut. On the Ruled surfaces in Minkowski 3-space R13. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(3 ): 8-.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2006.A0326     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2006/V7/I3 /8

[1] FU Ke-ang, ZHANG Li-xin. Precise asymptotics in the law of the logarithm for random fields in Hilbert space[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(4): 651-659.
[2] LIN Zheng-yan, SHEN Xin-mei. A note on strong law of large numbers of random variables[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(6): 1088-1091.
[3] JIANG Yue-xiang. Extreme value distributions of mixing two sequences with the same MDA[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(3): 335-342.
[4] LIN Zheng-yan, ZHANG Li-xin. Adaptive designs for sequential experiments[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2003, 4(2): 214-220.
[5] WEN Ji-wei. ALMOST SURE CONTINUITY OF INFINITE SERIES OF INDEPENDENT TWO-PARAMETER ORNSTEIN-UHLENBECK PROCESSES[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2001, 2(3): 253-256.
[6] ZHANG Li-xin, WEN Ji-wei. A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2001, 2(1): 79-83.
[7] JIANG Yue-xiang. A class of not max-stable extreme value distributions[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 4): 11-.
[8] Jiang Yue-xiang. More general results on mixed extreme value distributions*[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 7): 27-.
[9] JIANG Yue-xiang. Extreme value distributions of mixing two sequences with different MDA\'s[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(5): 509-517.