ON THE MOTION OF THE FRENET VECTORS AND TIMELIKE RULED SURFACES IN THE MINKOWSKI 3-SPACE.

Year 2000, Issue: 001, 247 - 254, 15.01.2000

Yusuf Yaylı

Abstract

In this paper, we obtained the distribution parameter of a

timelike ruled surface generated by a timelike straight line in Frenet

trihedron moving along a space-like curve. We show that the timelike

ruled surface is developable if and only if the base curve is a helix

(inclened curve). Furthermore, some theorems are given for the special

cases which the line is being the principal normal and binormal of the

base curve. In addition, it is shown that when the base curve is the same

as the striction curve, the ruled surface is not developable.

MINKOWSKI 3-UZAYINDA FRENET EKTORLERiNiN HAREKETi VE TIME-LIKE REGLE YUZEYLER

Abstract

Bu caltsmada bir space-like egri boyunca, Frenet iif yialusunde

altnan sabit bir dogrunun hareketiyle olusan time-like regle yiizeyin

dagilma parametresi hesaplandt. Regie yuzeyin dayanak egrisinin

helis olmasi halinde yuzeyin actlabilir oldugunu gosterdik. Ayrtca, sabit

dogrunun; dayanak egrisinin tegeti, normali, binormali v.s. olmasi

halinde bazt teoremler verdik. Daha fazlast, dayanak egrisinin,

striksiyon cizgisi olmast halinde, regIe yuzeyinin acilabilir olmadigtni

gosterdik.

Keywords

minkowski 3-uzayı, frenet ektörleri

References

• [1] Beem, 1.K. and Ehrlich. P.E., Global Lorentzian Geometry, Marcel Dekker. Inc. New York, 1981.
• [2] Hacisalihoglu, H.H and Turgut, A. On the distirbution parameter of timelike ruled surfaces in the Minkowski 3-space Far. East 1.Math sci 5(2) 1997, 321-328
• [3] Hacisalihoglu, H.H. Diferensiyel Geometri II. Cilt. A.U. Fen. Fak. 1994
• [4] Ikawa, T. On curves and sub manifolds in an indefinite-Riemannian Manifold. Tsukaba J. Math 9(2) 1985 353-371.
• [5] Ugurlu, H.H., Topal, A. "Relation Between Darboux Instantaneous Rotation Vectors of Curves on a Time-like Surface" Mathematical ancl Computational Applications, Vol. I. No 2 pp. 149-157 (1996).