Research Article
Surface family with a common natural geodesic lift of a spacelike curve with timelike binormal in Minkowski 3-space
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
Abstract
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | February 5, 2019 |
| Published in Issue | Year 2019 Volume: 1 Issue: 1 |
