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ON THE SCALAR AND DUAL FORMULATIONS OF THE CURVATURE THEORY OF LINE TRAJECTORIES IN THE LORENTZIAN SPACE
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 Title & Authors
ON THE SCALAR AND DUAL FORMULATIONS OF THE CURVATURE THEORY OF LINE TRAJECTORIES IN THE LORENTZIAN SPACE
Ayyildiz, Nihat; Yucesan, Ahmet;
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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.
 Keywords
Disteli axis;ruled surface;asymptotic normal;the central normal surface;dual Lorentzian space;Frenet frame;
 Language
English
 Cited by
1.
A STUDY ON A RULED SURFACE WITH LIGHTLIKE RULING FOR A NULL CURVE WITH CARTAN FRAME,;;

대한수학회보, 2012. vol.49. 3, pp.635-645 crossref(new window)
1.
On Motion of Robot End-Effector Using the Curvature Theory of Timelike Ruled Surfaces with Timelike Rulings, Mathematical Problems in Engineering, 2008, 2008, 1  crossref(new windwow)
2.
A STUDY ON A RULED SURFACE WITH LIGHTLIKE RULING FOR A NULL CURVE WITH CARTAN FRAME, Bulletin of the Korean Mathematical Society, 2012, 49, 3, 635  crossref(new windwow)
 References
1.
K. Akutagawa and S. Nishikawa, The Gauss Map and Spacelike Surfaces with Prescribed Mean Curvature in Minkowski 3-Space, Tohoku Math. J. (2) 42 (1990), no. 1, 67-82 crossref(new window)

2.
G. S. Birman and K. Nomizu, Trigonometry in Lorentzian Geometry, Amer. Math. Monthly 91 (1984), no. 9, 543-549 crossref(new window)

3.
H. Guggenheimer, Diffential Geometry, Dover Publications, 1977

4.
J. M. McCarthy, On the Scalar and Dual Formulations of the Curvature Theory of Line Trajectories, Journal of Mechanisms, Transmissions, and Automation in Design 109 (1987), 101-106 crossref(new window)

5.
J. M. McCarthy and B. Roth, The Curvature Theory of Line Trajectories in Spatial Kinematics, ASME Journal of Mechanical Design 103 (1981), no. 4, 718{724 crossref(new window)

6.
B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Aca- demic Press, London, 1983

7.
A. Turgut and H. H. Hacisalihoglu, Timelike Ruled Surfaces in the Minkowski 3-Space-II, Turkish J. Math. 22 (1998), no. 1, 33-46

8.
H. H. Ugurlu and A. Cahskan, The Study Mapping for Directed Spacelike and Timelike Lines in Minkowski 3-space ${\Re}^3_1$, Mathematical and Computational Applications 1 (1996), no. 2, 142-148

9.
G. R. Veldkamp, On the use of dual numbers, vectors and matrices in instan- taneous, spatial kinematics, Mechanism and Machine Theory 11 (1976), no. 2, 141-158 crossref(new window)

10.
Y. Yayh, A. Cahskan, and H. H. Ugurlu, The E. Study Maps of Circles on Dual Hyperbolic and Lorentzian Unit Spheres $H^2_0$ and $S^2_1$, Math. Proc. R. Ir. Acad. 102A (2002), no. 1, 37-47