International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2528

Full Length Research Paper

Properties of Bertrand curves in dual space

Ä°lkay ARSLAN GÃœVEN
  • Ä°lkay ARSLAN GÃœVEN
  • Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Åžehitkamil, 27310, Gaziantep, Turkey.
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Ä°pek AÄžAOÄžLU
  • Ä°pek AÄžAOÄžLU
  • Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Åžehitkamil, 27310, Gaziantep, Turkey.
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R. A. Sventkovsky
  • R. A. Sventkovsky
  • Technical Sciences, CITiS, Presnenskii val str., 19, Moscow 123557, Russia
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  •  Received: 08 November 2013
  •  Accepted: 19 February 2014
  •  Published: 16 May 2014

Abstract

Starting from ideas and results given by Özkaldi, Ä°larslan and Yaylı in (2009), in this paper we investigate Bertrand curves in three dimensional dual space D3. We obtain the necessary characterizations of these curves in dual space D3. As a result, we find that the distance between two Bertrand curves and the dual angle between their tangent vectors are constant. Also, well known characteristic property of Bertrand curve in Euclid space E3 which is the linear relation between its curvature and torsion is satisfied in dual space as λ.κ(S) + μ.τ(S) = 1. We show that involute curves, which are the curves whose tangent vectors are perpendicular, of a curve constitute Bertrand pair curves.

Key words: Bertrand curves, involute-evolute curves, dual space.

 

2000 Mathematics Subject Classification: 53A04 , 53A25 , 53A40.