Surface family with a common natural geodesic lift of a spacelike curve with timelike binormal in Minkowski 3-space

Yıl 2019, Cilt: 1 Sayı: 1, 17 - 23, 05.02.2019

Ergin Bayram , Evren Ergün , Emin Kasap

https://izlik.org/JA29CM58EE

Öz

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.

Anahtar Kelimeler

Surface family , natural lift , geodesic , spacelike curve , Minkowski 3-space

Kaynakça

• 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).