Research Article
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.
References
- Bayram E, Güler F, Kasap E, 2012. Parametric representation of a surface pencil with a common asymptotic curve. Comput. Aided Des., 44: 637-643.
- 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.
- Ergün E, Çalışkan M, 2011. On geodesic sprays In Minkowski 3-space. Int. J. Contem. Math. Sci., 6, (39): 1929-1933.
- 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.
- Ergün E, Bayram E, 2016. Surface Family with a Common Natural Geodesic Lift. International J.Math. Combin., 1: 34-41.
- 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.
- Kasap E, Akyıldız FT, Orbay K, 2008. A generalization of surfaces family with commonspatial geodesic. Appl. Math. Comput., 201: 781-789.
- 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.
- O'Neill B, 1983. Semi-Riemannian Geometry With Applications to Relativity. Academic Press, New York.
- Önder M, Uğurlu HH, 2013. Frenet frames and invariants of timelike ruled surfaces. Ain Shams Engineering Journal, 4: 502-513.
- Ratcliffe JG, 1994. Foundations of Hyperbolic Manifolds. Springer-Verlag, New York.
- Walrave J, 1995. Curves and surfaces in Minkowski space. PhD. Thesis, K. U. Leuven Faculteit Der Wetenschappen.
- 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.
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.
References
- Bayram E, Güler F, Kasap E, 2012. Parametric representation of a surface pencil with a common asymptotic curve. Comput. Aided Des., 44: 637-643.
- 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.
- Ergün E, Çalışkan M, 2011. On geodesic sprays In Minkowski 3-space. Int. J. Contem. Math. Sci., 6, (39): 1929-1933.
- 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.
- Ergün E, Bayram E, 2016. Surface Family with a Common Natural Geodesic Lift. International J.Math. Combin., 1: 34-41.
- 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.
- Kasap E, Akyıldız FT, Orbay K, 2008. A generalization of surfaces family with commonspatial geodesic. Appl. Math. Comput., 201: 781-789.
- 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.
- O'Neill B, 1983. Semi-Riemannian Geometry With Applications to Relativity. Academic Press, New York.
- Önder M, Uğurlu HH, 2013. Frenet frames and invariants of timelike ruled surfaces. Ain Shams Engineering Journal, 4: 502-513.
- Ratcliffe JG, 1994. Foundations of Hyperbolic Manifolds. Springer-Verlag, New York.
- Walrave J, 1995. Curves and surfaces in Minkowski space. PhD. Thesis, K. U. Leuven Faculteit Der Wetenschappen.
- 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.
There are 13 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Matematik / Mathematics |
| Authors | |
| Publication Date | June 1, 2019 |
| Submission Date | November 21, 2018 |
| Acceptance Date | February 8, 2019 |
| Published in Issue | Year 2019 Volume: 9 Issue: 2 |