3-Boyutlu Minkowski Uzayında Timelike Binormalli Spacelike Eğrinin Tabii Liftini Asimptotik Kabul Eden Yüzey Ailesi

Abstract

 timelike binormalli spacelike bir eğri,  ise  nın tabii lifti olsun. Bu çalışmada, 3 boyutlu Minkowski uzayında  yi ortak asimptotik eğri kabul eden yüzey ailesi elde edildi.  nin oluşturulan yüzeyler üzerinde asimptotik eğri olması için gerekli şartlar bulundu. Bazı örnekler verildi.

Keywords

• Yüzey Ailesi,Tabii Lift,Asimptotik Eğri,3-Boyutlu Minkowski Uzayı

Surface Family With a Common Natural Asymptotic Lift of a Spacelike Curve with Timelike Binormal in Minkowski 3-Space

Abstract

Let   be a spacelike curve with timelike binormal and   be its natural lift. In this work, we find surfaces accepting   as an asymptotic curve in  . We obtain sufficient constraints such that   is an asymptotic curve on the constructed surface. We present some illustrative examples.

Keywords

• Surface Family,Natural Lift,Asymptotic Curve,Minkowski 3-Space

References

1. Bayram E, Güler F, Kasap E, 2012. Parametric representation of a surface pencil with a common asymptotic curve. Comput. Aided Des., 44: 637-643.
2. Ergün E, Bayram E, Kasap E, 2014. Surface pencil with a common line of curvature in Minkowski 3-space. Acta Math. Sin. (Engl. Ser.), 30 (12): 2103-2118.
3. Ergün E, Çalışkan M, 2011. On geodesic sprays In Minkowski 3-space. Int. J. Contem. Math. Sci., 6, (39): 1929-1933.
4. Ergün E, Bayram E, Kasap E, 2015. Surface Pencil with a Common Natural Line of Curvature Lift. Journal of Science and Arts, 4 (33): 321-328.
5. Ergün E, Bayram E, 2016. Surface Family with a Common Natural Geodesic Lift. International J.Math. Combin., 1: 34-41.
6. Bayram E, Ergün E, 2016. Surface Family with a Common Natural Asymptotic Lift of a Timelike Curve in Minkowski 3-space. CBU Journal of Science, 12 (2): 209-214.
7. Kasap E, Akyıldız FT, Orbay K, 2008. A generalization of surfaces family with commonspatial geodesic. Appl. Math. Comput., 201: 781-789.
8. Li CY, Wang RH, Zhu CG, 2011. Parametric representation of a surface pencil with a common line of curvature. Comput. Aided Des., 43 (9): 1110-1117.

9. O'Neill B, 1983. Semi-Riemannian Geometry With Applications to Relativity. Academic Press, New York.
10. Önder M, Uğurlu HH, 2013. Frenet frames and invariants of timelike ruled surfaces. Ain Shams Engineering Journal, 4: 502-513.
11. Ratcliffe JG, 1994. Foundations of Hyperbolic Manifolds. Springer-Verlag, New York.
12. Walrave J, 1995. Curves and surfaces in Minkowski space. PhD. Thesis, K. U. Leuven Faculteit Der Wetenschappen.
13. Wang GJ, Tang K, Tai CL, 2004. Parametric representation of a surface pencil with a common spatial geodesic. Comput. Aided Des., 36 (5): 447-59.