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Journals / Journal of Scientific Reports-A / 2000 / Sayı: 001

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

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

Yusuf YAYLI
Pages
247–254
Publication Date
2000-01-15
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In addition, it is shown that when the base curve is the sameas the striction curve, the ruled surface is not developable.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we obtained the distribution parameter of atimelike ruled surface generated by a timelike straight line in Frenettrihedron moving along a space-like curve.
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Key Findings & Data:We show that the timelikeruled surface is developable if and only if the base curve is a helix(inclened curve).
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Conclusion & Impact:In addition, it is shown that when the base curve is the sameas the striction curve, the ruled surface is not developable.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:minkowski 3-uzayı · frenet ektörleri

Abstract

In this paper, we obtained the distribution parameter of atimelike ruled surface generated by a timelike straight line in Frenettrihedron moving along a space-like curve. We show that the timelikeruled surface is developable if and only if the base curve is a helix(inclened curve). Furthermore, some theorems are given for the specialcases which the line is being the principal normal and binormal of thebase curve. In addition, it is shown that when the base curve is the sameas the striction curve, the ruled surface is not developable.

Özet

Bu caltsmada bir space-like egri boyunca, Frenet iif yialusundealtnan sabit bir dogrunun hareketiyle olusan time-like regle yiizeyindagilma parametresi hesaplandt. Regie yuzeyin dayanak egrisininhelis olmasi halinde yuzeyin actlabilir oldugunu gosterdik. Ayrtca, sabitdogrunun; dayanak egrisinin tegeti, normali, binormali v.s. olmasihalinde bazt teoremler verdik. Daha fazlast, dayanak egrisinin,striksiyon cizgisi olmast halinde, regIe yuzeyinin acilabilir olmadigtnigosterdik.

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Cite This Article

YAYLI, Y. (2000). ON THE MOTION OF THE FRENET VECTORS AND TIMELIKE RULED SURFACES IN THE MINKOWSKI 3-SPACE.. Journal of Scientific Reports-A, Sayı: 001, 247–254. https://ajindex.com/articles/779557

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References (3)

  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
  3. 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).