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http://dx.doi.org/10.4134/JKMS.2006.43.6.1339

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)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.6, 2006 , pp. 1339-1355 More about this Journal
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;
Citations & Related Records

Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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