The Characterizations For The Spherical Images of Timelike W-Curves in Minkowski Space-Time

Yıl 2020, Cilt: 22 Sayı: 64, 59 - 66, 24.01.2020

Süha Yılmaz

https://doi.org/10.21205/deufmd.2020226407

Öz

We know that W-curve is a curve
which has constant Frenet curvatures. In this study, firstly, we have investigated
the principal normal and binormal spherical images of a timelike W-curve on
pseudohyperbolic space  in Minkowski space-time . Besides, the binormal spherical image
of the timelike W-curve is a spacelike curve which lies on pseudohyperbolic
space  Hence, we have obtained the Frenet-Serret
invariants of the mentioned image curve in terms of the invariants of the timelike
W-curve in the same space. Finally, we have given some characterizations of the
spherical image in the case of being helix for the timelike W-curve in
Minkowski space-time .

Anahtar Kelimeler

Spherical Images, Timelike W-Curve, General Helix

Kaynakça

• 1- O’Neill, B. 1983. Semi-Riemannian Geometry with Applications to Relativity, Academic Press Inc., London.
• 2- Milman, R.S., Parker, G.D. 1977. Elements of Differential Geometry, Prentice-Hall Inc., Englewood Cliffs, New Jersey.
• 3- Walrave, J. 1995. Curves and Surfaces in Minkowski Space, Dissertation, K.U. Leuven, Fac. of Science, Leuven, 147p.
• 4- Yılmaz, S. 2001. Spherical Indicators of Curves and Characterizations of Some Special Curves in Four Dimensional Lorentzian Space L^4, Dissertation, Dokuz Eylül University, İzmir
• 5- Yılmaz, S., Turgut, M. 2008. On the Differential Geometry of the Curves in Minkowski Space-Time I, International Journal of Contemporary Mathematical Sciences Volume 3, pp. 1343-1349.
• 6- Yılmaz, S., Özyılmaz, E., Turgut, M. 2009. On the Differential Geometry of the Curves in Minkowski Space-Time II, International Journal of Contemporary Mathematical Sciences Volume 3, pp. 53-55.
• 7- Yılmaz, S., Özyılmaz, E., Yaylı, Y., Turgut, M. 2010. Tangent and Trinormal Spherical Images of a Time-Like Curve on the Pseudohyperbolic Space, Proceedings of the Estonian Academy of Sciences, Volume 59 No 3, pp. 216-224.
• 8- Bonnor, W.B. 1969. Null Curves in Minkowski Space-Time, Tensor, Volume 20, pp. 229-242. Petrovic-Torgasev, M., Sucurovic, E. 2002. W-Curves in Minkowski Space-Time, Novi Sad Journal of Mathematics, Volume 32, No 2, pp. 55-65. Lopez, R. 2010. Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space, International Electronic Journal of Geometry, Volume 3, No 2, pp. 67-101.9- Ratcliffe, J.G. 2006. Foundations of Hyperbolic Manifolds, Springer Science-Business Media, LLC, New York, pp. 68-72.
• 10- Monterde, J. 2007. Curves with Constant Curvature Ratios, Boletin de la Sociedad Matematica Mexicana,, Volume 3, pp. 177-186.
• 11- Öztürk, G., Arslan, K., Hacısalihoğlu H.H. 2008. A Characterization of CCR-Curves in R^m, Proceedings of the Estonian Academy of Sciences, Volume 57, pp. 217-224.
• 12-İlarslan, K., Boyacıoğlu, Ö. 2007. Position Vectors of a Spacelike W-Curve in Minkowski 3-Space E_1^3, Volume 44, No 3, pp. 429-438. Camcı, Ç., İlarslan, K., Sucurovic, E. 2003. On Pseudohyperbolic Curves in Minkowski Space-Time, Turkish Journal of Mathematics, Volume 27, pp. 315-328.