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On the Ruled surfaces in Minkowski 3-space R13
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Öğrenmiş Alper Osman, Balgetir Handan, Ergüt Mahmut. On the Ruled surfaces in Minkowski 3-space R13[J]. Journal of Zhejiang University Science A, 2006, 7(3): 326-329.
@article{title="On the Ruled surfaces in Minkowski 3-space R13",
author="Öğrenmiş Alper Osman, Balgetir Handan, Ergüt Mahmut",
journal="Journal of Zhejiang University Science A",
volume="7",
number="3",
pages="326-329",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A0326"
}
%0 Journal Article
%T On the Ruled surfaces in Minkowski 3-space R13
%A Ö
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%A Balgetir Handan
%A Ergü
%A t Mahmut
%J Journal of Zhejiang University SCIENCE A
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%P 326-329
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A0326
TY - JOUR
T1 - On the Ruled surfaces in Minkowski 3-space R13
A1 - Ö
A1 - ğ
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A1 - Alper Osman
A1 - Balgetir Handan
A1 - Ergü
A1 - t Mahmut
J0 - Journal of Zhejiang University Science A
VL - 7
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SP - 326
EP - 329
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A0326
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.
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[6] Jung, S.D., Pak, J.S., 1996. Classification of cylindrical Ruled surfaces satisfying ΔH=AH in a 3-dimensional Minkowski space. Bull. Korean Math. Soc., 33(1):97-106.
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[8] Turgut, A., Hacısalihoğlu, H.H., 1998. Timelike Ruled surfaces in the Minkowski 3-space-II. Tr. J. of Mathematics, 22:33-46.
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