Skip to main content
SpringerLink
Log in

On the ruled surfaces in Minkowski 3-space R 1 3

  • Published:
Journal of Zhejiang University-SCIENCE A Aims and scope Submit manuscript

Abstract

Izumiya and Takeuchi (2003) obtained some characterizations for Ruled surfaces. Turgut and Hacisalihoğlu (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 R 1 3. 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Turgut, A., Hacisalihoğlu, H.H., 1998. Timelike Ruled surfaces in the Minkowski 3-space-II. Tr. J. of Mathematics, 22:33–46.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Firat University, Elaziğ, Turkey

    Öǧrenmiş Alper Osman, Balgetir Handan & Ergüt Mahmut

Authors
  1. Öǧrenmiş Alper Osman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Balgetir Handan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ergüt Mahmut
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Öǧrenmiş, A.O., Balgetir, H. & Ergüt, M. On the ruled surfaces in Minkowski 3-space R 1 3 . J. Zhejiang Univ. - Sci. A 7, 326–329 (2006). https://doi.org/10.1631/jzus.2006.A0326

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/jzus.2006.A0326

Key words

Search

Navigation