African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 245

Full Length Research Paper

On integral invariants of ruled surface generated by the Darboux frame of the transversal intersection timelike curve of two timelike surfaces in Lorentz-Minkowski 3-space

ENGİN AS
  • ENGİN AS
  • Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, 55139-Kurupelit, Samsun, Turkey
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AYHAN SARIOĞLUGİL
  • AYHAN SARIOĞLUGİL
  • Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, 55139-Kurupelit, Samsun, Turkey
  • Google Scholar


  •  Received: 20 January 2014
  •  Accepted: 16 March 2014
  •  Published: 30 April 2014

Abstract

In this paper, some characteristic properties of ruled surfaces which are generated by the Darboux frame of the transversal intersection timelike curve of two timelike surfaces were studied in Lorentz-Minkowski 3-Space . Moreover, the relations between the Darboux frames, the Darboux derivate formulas, the apex angles, the pitchs, the geodesic curvatures, the normal curvatures, the geodesic torsions and the dralls of the ruled surfaces were given. Then, some characterizations were investigated for the transversal intersection curves. Namely, in the case of the intersection curves were geodesic lines and asymptotic lines, some corollaries were investigated. Lastly, examples were given and the figures were drawn using Maple.

 

Key words. Transversal intersection spaclike curve, ruled surface, geodesic curvatures.