On the developable ruled surfaces Kinematically generated in Minkowski 3-Space

HACI BAYRAM KARADAg١, EROL KILIC, MUGEKAR ADAg١

Abstract


In this paper, we present a method to be developable of a ruled surface, generated in Minkowski 3-space R corresponding to the dual Lorentzian curves according to E. Study's transference principle and some theorems and examples.


Keywords


Ruled surfaces; dual vector; lorentzian dual unit sphere; hyperbolic dual unit sphere; minkowski space

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References


Chen, H. Y. & Pottmann, H. 1999. Approximation by ruled surfaces, Journal of Computational and Applied Mathematics 102: 143-153.

Haclu, H. H. 1972. On the pitch of a closed ruled surfaces, Mechanism and Machine Theory, 7:291-305.

Karadag, H. B. & Keles, S. 2005. On the integral invariants of kinematically generated ruled surfaces, Indian Journal of Science and Technologies Translation. A, Vol. 29:No.A3, 3455-470.

Kim, Y. H. & Yoon, D. W. 2004. Classification of ruled surface in minkowski 3-spaces, Journal of Geometry and Physics, Vol. 49: No.1, 89-100.

KÎse, Ú. 1999. A method of determination of a developable ruled surface, Mechanism and Machine Theory, 34: 1187-1193. MÏller, H. R. 1980. Ûber Îffnungsma e Kinematisch erzeugter geschlossener regelflachen, Abhandl. Braunschw. Wiss. Ges., 40: 7-16.

O'Neill, B. 1983. Semi-riemannian geometry with applications to relativity, Academic Press, New York.

Schaaf, J. A. & Ravani, B. 1998. Geometric continuity of ruled surface, Computer Aided Geometric Design, 15: 289-310.

Study, E., 1891. Von den bewegungen und umblegungen, mathem. Annalen, 39: 441-564.

Turgut, A. & Hacsalihoglu, H. H. 1998. Timelike ruled surfaces in the minkowski 3-space-II, Turkish Journal of Mathematics, 22: 33-46.

Veldkamp, G. R. 1976. On the use of dual numbers, Vectors and Matrices in Instantaneous, Spatial Kinematics, Mechanism and Machine Theory, 11: 141-156.


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