# ON THE SCALAR AND DUAL FORMULATIONS OF THE CURVATURE THEORY OF LINE TRAJECTORIES IN THE LORENTZIAN SPACE

• Ayyildiz, Nihat ;
• Yucesan, Ahmet
• Published : 2006.11.01
• 104 34

#### 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.

#### Keywords

Disteli axis;ruled surface;asymptotic normal;the central normal surface;dual Lorentzian space;Frenet frame

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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