International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2572

Full Length Research Paper

Translation surfaces according to Frenet frame in Minkowski 3-space

Muhammed Çetin1*, Hüseyin KocayiÄŸit2 and Mehmet Önder2
1Instutition of Science and Technology, Celal Bayar University, Manisa, Turkey. 2Department of Mathematics, Faculty of Arts and Science, Celal Bayar University, Manisa, Turkey.
Email: [email protected]

  •  Accepted: 23 November 2012
  •  Published: 16 December 2012

Abstract

In this paper, using non-planar space curves, the translation surfaces were investigated according to Frenet frames in Minkowski 3-space and some properties of these surfaces were given. Furthermore, we calculated first fundamental form, second fundamental form, Gaussian curvature and mean curvature of the translation surface. Also, the Darboux frame of the generator curves of the translation surfaces in Minkowski 3-space was given. Finally, we gave the conditions of being a geodesic, an asymptotic line and a principal line for the generator curves of the translation surface.

 

Key words: Darboux frame, Minkowski 3-space, translation surface.