Canal Surface Around A Spacelike Focal Curve In Lorentz 3-Space

Yıl 2018, Cilt: 22 Sayı: 2, 608 - 614, 15.08.2018

Abdullah Yıldırım

Öz

In this paper, we study the tubular surface around  a spacelike focal curve in Lorentz 3-Space. First for better understanding of the subject, the definitions and equations of the canal surface around a regular curve in 3-dimensional Euclidean space  are given. Section 3, concerned with some important definitions and theorems about focal curves in 3-dimensional Lorentz space. In section 4, we derive equations for canal and tubular surfaces around a spacelike focal curve in 3-dimensional Lorentz. Then we obtain the first and the second fundamental forms  on the tubular surfaces in the same space. Gauss and mean curvatures of this surface are obtained. Finally, in this space it is investigated if the parameter curves for the tubular surface are geodesic or asymptotic and related theorems about them are stated and proved.

Anahtar Kelimeler

Canal surfaces, Tubular surfaces; Focal curvatures; Lorentz space

Kaynakça

• [1] Doğan, F., Yaylı, Y. 2011. On the curvatures of tubular surface with Bishop frame. Commun. Fac. Sci. Univ. Ank. Series A1 Volume 60 (1) ( 2011 ), 59-69.
• [2] Hacısalihoğlu, H. H. 2000. Differensiyel Geometri II. Hacısalihoğlu Yayınları, 45-46.
• [3] Karacan, M. K., Bukcu, B. 2007. An alternative moving frame for tubular surfaces around spacelike curves with a spacelike Binormal in the Minkowski 3-space. Mathematica Moravica, Volume 11, 47-54.
• [4] Kühnel, W. 2003. Differential Geometry Curves- Surfaces-Manifolds, Second ed. Friedr. Vieweg & Sohn Verlag, 380 p.
• [5] Oprea, J. 1997. Differential Geometry and Its Applications. Prentice-Hall Inc, 78-80.
• [6] Özdemir, M., Ergin, A. A. 2007. Spacelike Darboux curves in Minkowski 3-space. Differential Geometry-Dynamical Systems, vol. 9, 131-137.
• [7] Petrovic, M., Sucurovic, E. 2000. Some characterizations of the spacelike, the timelike and the null curves on the pseudohyperbolic space H20 in E31. Kragujevac J.Math, vol 22, 71-82.
• [8] Uribe-Vargas, R. 2005. On vertices focal curvatures and differential geometry of space curves. Bull. Brazilian Math. Soc. 36 (3), 285–307.
• [9] Yıldırım, A. 2016. Tubular surface around a Legendre curve in BCV spaces. New Trends in Mathematical Sciences, 4(2), 61-71.(04:10:2017)