Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE SCALAR AND DUAL FORMULATIONS OF THE CURVATURE THEORY OF LINE TRAJECTORIES IN THE LORENTZIAN SPACE

  • Ayyildiz, Nihat (Department of Mathematics University of Suleyman Demirel) ;
  • Yucesan, Ahmet (Department of Mathematics University of Suleyman Demirel)
  • Published : 2006.11.01
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Abstract

This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.

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References

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Cited by

  1. On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings vol.2008, 2008, https://doi.org/10.1155/2008/362783
  2. A STUDY ON A RULED SURFACE WITH LIGHTLIKE RULING FOR A NULL CURVE WITH CARTAN FRAME vol.49, pp.3, 2012, https://doi.org/10.4134/BKMS.2012.49.3.635