# New Horizons in Mathematical Physics

### Null Curves and Representation in Three Dimensional Minkowski Spacetime

Download PDF (513.1 KB) PP. 1 - 13 Pub. Date: June 23, 2017

### Author(s)

**Huili Liu**^{*}

Department of Mathematics, Northeastern University, China**Seoung Dal Jung**

Department of Mathematics and Research Institute for Basic Sciences, Jeju National University, Korea

### Abstract

### Keywords

### References

[1] W. B. Bonnor, Null curves in a Minkowski space-time, Tensor (N. S.), 20(1969), 229-242.

[2] B. Y. Chen, When does the position vector of a space curve always lie in its rectifying plane, Amer. Math. Monthly, 110(2003), 147-152.

[3] G. Clément, Black holes with a null Killing vector in three-dimensional massive gravity, Classical Quantum Gravity, 26(2009), 165002(11pp).

[4] A. Ferrández, A. Giménez, P. Lucas, Null generalized helices in Lorentz-Minkowski spaces, J. Phys. A: Math. Gen., 35(2002), no. 39, 8243-8251.

[5] A. Ferrández, A. Giménez, P. Lucas, Geometrical particle models on 3D null curves Phys. Lett. B, 543(2002), 311-317.

[6] A. Ferrández, A. Giménez, P. Lucas, Relativistic particles with rigidity along light-like curves, In HORIZONS IN WORLD PHYSICS, Vol. 245, Ch. 6, Tori V. Lynch (Editor), Nova Science Publishers Inc., 2004, ISBN:1-59454-063-2.

[7] A. Ferrández, A. Giménez, P. Lucas, Relativistic particles and the geometry of 4d null curves, J. Geom. Phys.,57(10)(2007), 2124-2135.

[8] Jun-ichi Inoguchi, Sungwook Lee, Null curves in Monkowski 3-space, International Electronoc Journal of Geometry, 2(2008), 40-83.

[9] Huili Liu, Curves in the lightlike cone, Contrib. Algebr. Geom., 45(2004), 291-303.

[10] Huili Liu, Qingxian Meng, Representation formulas of curves in a 2 and 3 dimensional lightlike cone, Results Math., 59(2011), 437-451.

[11] Armen Nersessian, Large massive 4d particle with torsion and conformal mechanics, Physics Letters B, 473, Issues 1-2, 27 January 2000, Pages 94-101.

[12] Armen Nersessian, R. Manvelyan, H.J.W. Müller-Kirsten, Particle with torsion on 3d null-curves, Nuclear Physics B - Proceedings Supplements, Volume 88, Issues 1?C3, June 2000, Pages 381-384.

[13] Armen Nersessian, Eduardo Ramos, Massive spinning particles and the geometry of null curves, Phys. Lett.B, 445(1998), 123-128.

[14] Armen Nersessian, Eduardo Ramos, A geometrical particle model for anyons, Modern Phys. Lett. A, 14 (1999), No. 29, 2033-2037.

[15] A. D. Polyanin, V. F. Zaitsev Handbook of Exact Solutions for Ordinary Differential Equations, second edition, 2003, Chapman & Hall/CRC.