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Dergiler / Mathematical and Computational Applications / 2014 / Cilt: 19 - Sayı: 2

The darboux trihedrons of regular curves on a regular time-like surface

Emin ÖZYILMAZ
Sayfa
172–183
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The aim of this study is to investigate the formulae between the Darboux Vectors of the time-like curve ( ) c, the time-like parameter curve ${(C_1)}$ and the space-like parameter curve ${(C_2)}$ cwhich are not intersecting perpendicularly.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this work, we study Differential Geometry in the Minkowski 3-space $R_{3}^{1}$of the curves on a time-like regular surface by using parameter curves which are not perpendicular to each other.
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Temel Bulgular & Veri:In this work, we study Differential Geometry in the Minkowski 3-space $R_{3}^{1}$of the curves on a time-like regular surface by using parameter curves which are not perpendicular to each other.
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Sonuç & Katkı:The aim of this study is to investigate the formulae between the Darboux Vectors of the time-like curve ( ) c, the time-like parameter curve ${(C_1)}$ and the space-like parameter curve ${(C_2)}$ cwhich are not intersecting perpendicularly.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this work, we study Differential Geometry in the Minkowski 3-space $R_{3}^{1}$of the curves on a time-like regular surface by using parameter curves which are not perpendicular to each other. The aim of this study is to investigate the formulae between the Darboux Vectors of the time-like curve ( ) c, the time-like parameter curve ${(C_1)}$ and the space-like parameter curve ${(C_2)}$ cwhich are not intersecting perpendicularly.

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Bu Makaleye Atıf Yap

ÖZYILMAZ, E. (2014). The darboux trihedrons of regular curves on a regular time-like surface. Mathematical and Computational Applications, Cilt: 19 - Sayı: 2, 172–183. https://ajindex.com/articles/279786

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Kaynakça (8)

  1. H. Ugurlu, A. Çalışkan, The Space-like and Time-like Surface Geometry by the Darboux Vector, The press of the Celal Bayar Univ., 2012
  2. S. Yılmaz, E. Ozyilmaz, M. Turgut, On The Differential Geometry of the Curves in Minkowski Space-Time II, Int.jour. of Comput Math Sci 3(2), 2009
  3. Y. Yaylı, H.H. Hacısalihoğlu, Closed Curves in the Minkowski 3-space, Hadronic Journal 23(3), 2000
  4. S. Yılmaz, Spherical Indicators of Curves and Characterizations of some special curves in four dimensional Lorentzian Space, $L^{4}$, Ph.D.dissertation, Dept.Math.Dokuz Eylül Univ, İzmir, Turkey, 2001
  5. F. Akbulut, Bir Yüzey Üzerindeki Eğrilerin Darboux Vektörleri, E.Ü.Faculty of Science, İzmir, 1983
  6. S. Kızıltuğ, Y. Yaylı, Space-like Curve on Space-like Parallel Surface in Minkowski 3-space $E^{3}_{1}$, Int. J. Math. Comput. 19(2), 94–105, 2013
  7. A.T. Ali, R. Lopez, M. Turgut, k-type partially null and pseudo null slant helices in Minkowski 4-space, Mathematical Communications 17(1), 93-103, 2012
  8. J.G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer, 2006.