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Surface family with a common natural geodesic lift of a spacelike curve with timelike binormal in Minkowski 3-space
Year 2019 ,
Volume: 1 Issue: 1, 17 - 23, 05.02.2019
Ergin Bayram
,
Evren Ergün
,
Emin Kasap
Abstract
In this work we aim to find a surface family possessing the natural lift of a given spacelike curve with timelike
binormal as a geodesic in Minkowski 3-space. We express necessary and sufficient conditions for the given
curve such that its natural lift is a geodesic on any member of the surface family. Finally, we illustrate the method
with some examples.
References
O'Neill, B.: Semi-Riemannian Geometry With Applications to Relativity, Academic Press, New York, 1983.
Ratcliffe, J.G.: Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994.
Önder M., Uğurlu H.H., Frenet frames and invariants of timelike ruled surfaces, Ain Shams Engineering Journal, 4, 502-513 (2013).
Walrave J. 1995, Curves and surfaces in Minkowski space, PhD. Thesis, K. U. Leuven Faculteit Der Wetenschappen.
Ergün, E., Çalışkan, M, On geodesic sprays In Minkowski 3-space, Int. J. Contem. Math. Sci., 6, 39, 1929-1933 (2011).
Year 2019 ,
Volume: 1 Issue: 1, 17 - 23, 05.02.2019
Ergin Bayram
,
Evren Ergün
,
Emin Kasap
References
O'Neill, B.: Semi-Riemannian Geometry With Applications to Relativity, Academic Press, New York, 1983.
Ratcliffe, J.G.: Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994.
Önder M., Uğurlu H.H., Frenet frames and invariants of timelike ruled surfaces, Ain Shams Engineering Journal, 4, 502-513 (2013).
Walrave J. 1995, Curves and surfaces in Minkowski space, PhD. Thesis, K. U. Leuven Faculteit Der Wetenschappen.
Ergün, E., Çalışkan, M, On geodesic sprays In Minkowski 3-space, Int. J. Contem. Math. Sci., 6, 39, 1929-1933 (2011).
There are 5 citations in total.
Cite
APA
Bayram, E., Ergün, E., & Kasap, E. (2019). Surface family with a common natural geodesic lift of a spacelike curve with timelike binormal in Minkowski 3-space. Hagia Sophia Journal of Geometry, 1(1), 17-23.