Advances in Applied Clifford Algebras

, Volume 22, Issue 4, pp 939–953 | Cite as

On Some Characterizations of Ruled Surface of a Closed Timelike Curve in Dual Lorentzian Space

Article

Abstract

In this paper, we investigate the relations between the pitch, the angle of pitch and drall of parallel ruled surface of a closed curve in dual Lorentzian space.

Keywords

Timelike dual curve ruled surface Lorentzian space dual numbers 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Birman G.S., Nomizu K.: Trigonometry in Lorentzian Geometry. Am. Math. Mont. 91, 543–549 (1984)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Clifford W.K.: Preliminary Sketch of Biquaternions. Proc. London Math. Soc. 4, 361–395 (1873)Google Scholar
  3. 3.
    W. Blaschke, Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie. Band I. Elementare Differentialgeometrie. (German) 3d ed. Dover Publications, New York, 1945.Google Scholar
  4. 4.
    E. Study, Geometrie der Dynamen. Druck und Verlag von B. G. Teuner, Leipzig, 1903.Google Scholar
  5. 5.
    Gürsoy O.: The Dual Angle of Pitch of a Closed Ruled Surface. Mech. and Mach. Theory 25, 131–140 (1990)CrossRefGoogle Scholar
  6. 6.
    H. H. Hacısalihoğlu, Moving Geometry and Quaternion Theory. Publ. of Science and Art Faculty of Gazi University, Math. 2, Ankara, (1983), 338p (in Turkish).Google Scholar
  7. 7.
    Hacisalihoğlu H.H.: On the Pitch of a Closed Ruled Surface. Mech. and Mach. Theory 7, 291–305 (1972)CrossRefGoogle Scholar
  8. 8.
    H. H. Hacısalihoğlu, Differential Geometry. Publ. of Science and Art Faculty of Inonu University, Math. 2, Malatya (1983), 894p.Google Scholar
  9. 9.
    H. R.Müller, Kinematic Lessons. Publ. of Science Faculty of Ankara University, Math. 27, Ankara (1963), 292p (in Turkish).Google Scholar
  10. 10.
    J. G. Ratcliffe, Foundations of Hyperbolic Manifolds. Springer-Verlag, New York, (1994), 736p.Google Scholar
  11. 11.
    S. Şenyurt, Parallel Regle Surfaces and Properties of Some Characteristic. Institute of Science of Ondokuz Mayıs University, Ph. D. Thesis (1999).Google Scholar
  12. 12.
    A. Turgut, Spacelike and Timelike Ruled Surfaces in 3-dimensional Minkowski Space. Institute of Science of Ankara University, Ph. D. Thesis, (1995).Google Scholar
  13. 13.
    Uğurlu H.H.: On the Geometry of Timelike Surfaces. Commun. Fac. Sci. Ank. Series A1 46, 211–223 (1997)MATHGoogle Scholar
  14. 14.
    Uğurlu H.H., Çalışkan A.: The Study Mapping for Directed Spacelike and Timelike Lines in Minkowski 3-Space. Math. Comp. Appl. 1, 142–148 (1996)MATHGoogle Scholar
  15. 15.
    V. D. I. Woestijne, Minimal Surfaces of the 3-dimensional Minkowski Space. Proc. Congres “Géométrie Différentielle et Applications”, Avignon, Word Scientific Publishing. Singapore (1988), 344-369.Google Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Faculty of Art and Science, Department of MathematicsYildiz Technical UniversityEsenler, IstanbulTurkey
  2. 2.Faculty of Art and Science, Department of MathematicsOrdu UniversityOrduTurkey

Personalised recommendations