Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres
-
1787
Downloads
-
3178
Views
Authors
Jianguo Sun
- School of Science, China University of Petroleum (east China), Qingdao, 266555, P. R. China.
Donghe Pei
- School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China.
Abstract
The null curves on 3-null cone have the applications in the studying of horizon types. Via the pseudo-scalar
product and Frenet equations, the differential geometry of null curves on 3-null cone is obtained. In the local
sense, the curvature describes the contact of submanifolds with pseudo-spheres. We introduce the geometric
properties of the null curves on 3-null cone and unit semi-Euclidean 3-spheres, respectively. On the other
hand, we give the existence conditions of null Bertrand curves on 3-null cone and unit semi-Euclidean
3-spheres.
Share and Cite
ISRP Style
Jianguo Sun, Donghe Pei, Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 3, 275--284
AMA Style
Sun Jianguo, Pei Donghe, Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres. J. Nonlinear Sci. Appl. (2015); 8(3):275--284
Chicago/Turabian Style
Sun, Jianguo, Pei, Donghe. "Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres." Journal of Nonlinear Sciences and Applications, 8, no. 3 (2015): 275--284
Keywords
- Null Bertrand curve
- AW(k)-type curve
- Frenet frame
- null cone.
MSC
References
-
[1]
K. Arslan, C. Özgür , Curves and surfaces of AW(k)-type, in: Defever, F, J. M. Morvan, I. V. Woestijne, L. Verstraelen, G. Zafindratafa, (Eds.), Geometry and Topology of Submanifolds, World Scientific (1999)
-
[2]
H. Balgetir, M. Bektaş, M. Ergüt , Bertrand cuves for nonnull curves in 3 dimensional Lorentzian space , Hadronic Journal, 27 (2004), 229–236.
-
[3]
H. Balgetir, M. Bektaş, J. Inoguchi, Null Bertrand curves in Minkowski 3 space and their characterizations, Note di Matematica, 23 (2004), 7–13.
-
[4]
M. Barros, A. Ferrández, Null scrolls as solutions of a sigma model, J. Phys. A-Math. thoer., 45 (2012), 12 pages.
-
[5]
M. Campanelli, C. O. Lousto, Second order gauge invariant gravitational perturbations of a Kerr black hole, Phys. Rev. D, 59 (1999), 16 pages.
-
[6]
K. L. Duggal, D. H. Jin , Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, (2007)
-
[7]
S. Ersoy, A. Inalcik, On the generalized timelike Bertrand curves in 5-dimensional Lorentzian space, Differential Geom.-Dynamical Systems, 13 (2011), 78–88.
-
[8]
A. Ferrández, A. Giménez, P. Lucas, Geometrical particle models on 3D null curves, Phys. Lett. B, 543 (2002), 311–317.
-
[9]
M. Göçmen, S. Keleş, , arXiv preprint , arXiv:1104.3230 (2011)
-
[10]
K. Ilarslan, Ö. Boyacıoğlu, Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos Solitons Fractals, 38 (2008), 1383–1389.
-
[11]
L. L. Kong, D. H. Pei , On spacelike curves in hyperbolic space times sphere, Int. J. Geom. Methods Mod. Phys., 11 (2014), 12 pages.
-
[12]
C. Kozameh, P. W. Lamberti, O. Reula, Global aspects of light cone cuts, J. Math. Phys., 32 (1991), 3423–3426.
-
[13]
M. Külahcı, M. Ergüt , Bertrand curves of AW(k)-type in Lorentzian space, Nonlinear Anal., 70 (2009), 1725– 1731.
-
[14]
M. Külahcı, M. Bektaş, M. Ergüt , Curves of AW(k)-type in 3-dimensional null cone, Phys. Lett. A, 371 (2007), 275–277.
-
[15]
P. Lucas, J. A. Ortega-Yagües, Bertrand curves in the three-dimensional sphere, J. Geom. Phys., 62 (2012), 1903–1914.
-
[16]
B. O’Neill , Semi-Riemannian Geomerty with applications to relativity, Academic press, London (1983)
-
[17]
A. Neraessian, E. Ramos, Massive spinning particles and the geometry of null curves, Phys. Lett. B, 445 (1998), 123–128.
-
[18]
C. Özgür, F. Gezgin, On some curves of AW(k)-type, Differential Geom.-Dynamical systems, 7 (2005), 74–80.
-
[19]
H. B. Oztekin, Weakened Bertrand curves in the Galilean space G3, J. Adv. Math. Studies, 2 (2009), 69–76.
-
[20]
L. R. Pears, Bertrand curves in Riemannian space, J. London Math. Soc., 1 (1935), 180–183.
-
[21]
S. G. Papaioannou, D. Kiritsis , An application of Bertrand curves and surfaces to CADCAM , Comput. Aided Geom. Design, 17 (1985), 348–352.
-
[22]
R. A. Penrose, Remarkable property of plane waves in general relativity, Rev. Modern Phys., 37 (1965), 215–220.
-
[23]
J. G. Sun, D. H. Pei, Null Cartan Bertrand curves of AW(k)-type in Minkowski 4-space, Phys. Lett. A, 376 (2012), 2230–2233.
-
[24]
J. G. Sun, D. H. Pei, Families of Gauss indicatrices on Lorentzian hypersurfaces in pseudo-spheres in semi- Euclidean 4 space, J. Math. Anal. Appl., 400 (2013), 133–142.
-
[25]
J. G. Sun, D. H. Pei, Null surfaces of null curves on 3-null cone, Phys. Lett. A, 378 (2014), 1010–1016.
-
[26]
G. H. Tian, Z. Zhao, C. B. Liang, Proper acceleration' of a null geodesic in curved spacetime, Classical Quant. Grav., 20 (2003), 4329.
-
[27]
M. Y. Yilmaz, M. Bektaş, General properties of Bertrand curves in Riemann-Otsuki space, Nonlinear Anal., 69 (2008), 3225–3231.