Advances in Applied Clifford Algebras

, Volume 22, Issue 2, pp 499–510 | Cite as

On Developable Ruled Surfaces in Minkowski Space



The aim of this study is to obtain the distribution parameter of a ruled surface generated by a straight line in Frenet trihedron moving along two different spacelike curves with the same parameter. At this time, the Frenet frames of these curves are not the same. We have moved the director vector of the first curve along the second curve. It is shown that the ruled surface is developable if and only if the base curve is helix. In addition, some results and theorems are presented with special cases.


Frenet frame spacelike curve timelike vector 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beem J.K., Ehrlich P.E.: Global Lorentzian Geometry. Marcel Dekker Inc., New York (1981)MATHGoogle Scholar
  2. 2.
    Hacısalihoğlu H.H.: Differential Geometri. Ankara Üniversitesi, Fen Fakültesi (1993)Google Scholar
  3. 3.
    H. H. Hacısalihoğlu, Differential Geometri-II. A Ü., Fen Fak., 1994.Google Scholar
  4. 4.
    Hacısalihoğlu H.H., Turgut A.: On the Distribution Parameter of Spacelike Ruled Surfaces in the Minkowski 3-space. Far East J. Math Sci 5, 321–328 (1997)MathSciNetMATHGoogle Scholar
  5. 5.
    R. Lopez, Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space. \(\tt[arXiv:0810.3351v1]\) math.DG.Google Scholar
  6. 6.
    Özyılmaz E., Yaylı Y., (2000) On the Closed Motions and Closed Spacelike Ruled Surfaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 49: 49-58Google Scholar
  7. 7.
    Ikawa T.: On Curves and Submanifolds in an Indefinnite-Riemannian Manifold. Tsukaba J. Math 9, 353–371 (1985)MathSciNetMATHGoogle Scholar
  8. 8.
    Yaylı Y., Saracoglu S., On Developable Ruled Surfaces. Advances in Geometry (submitted).Google Scholar
  9. 9.
    Yaylı Y.: On The Motion of the Frenet Vectors and Spacelike Ruled Surfaces in the Minkowski 3-Space. Mathematical & Computational Applications 5, 49–55 (2000)MathSciNetGoogle Scholar
  10. 10.
    Ali A.T.: Spacelike Salkowski and anti-Salkowski Curves with a Spacelike Principal Normal in Minkowski 3-Space. Int. J. Open Problems Comp. Math. 2, 451–460 (2009)MATHGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Faculty of Science, Department of MathematicsAnkara UniversityAnkaraTurkey
  2. 2.Faculty of Science and Arts, Department of MathematicsSiirt UniversitySiirtTurkey

Personalised recommendations