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Received: 2005-09-20

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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.3 P.326~329

http://doi.org/10.1631/jzus.2006.A0326


On the Ruled surfaces in Minkowski 3-space R13


Author(s):  Ö,ğ,renmiş, Alper Osman, Balgetir Handan, Ergü,t Mahmut

Affiliation(s):  Department of Mathematics, Faculty of Arts and Sciences, Fı more

Corresponding email(s):   aogrenmis@firat.edu.tr

Key Words:  Timelike Ruled surfaces, Bertrand curve, Cylindrical helices


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.

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author="Öğrenmiş Alper Osman, Balgetir Handan, Ergüt Mahmut",
journal="Journal of Zhejiang University Science A",
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doi="10.1631/jzus.2006.A0326"
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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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Reference

[1] Balgetir, H., Bektaş, M., Ergüt, M., 2004. Bertrand curves for Nonnull curves in 3-dimensional Lorentzian space. Hadronic Journal, 27:229-236.

[2] Beem, J.K., Ehrlich, P.E., 1981. Global Lorentzian Geometry. Marcell Decker, Inc., New York.

[3] Choi, S.M., 1995. On The Gauss map of Ruled surfaces in a 3-dimensional Minkowski space. Tsukuba J. Math., 19(2):285-304.

[4] Ikawa, T., 1985. On curves and submanifolds in an indefinite-Riemannian manifold. Tsukuba J. Math., 9:353-371.

[5] Izumiya, S., Takeuchi, N., 2003. Special curves and Ruled surfaces. Beitrage zur Algebra und Geometrie Contributions to Algebra and Geometry, 44(1):203-212.

[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.

[7] O’Neill, B., 1983. Semi-Riemannian Geometry with Applications to Relativity. Academic Press, New York.

[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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