Geodesic
Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres
Sun, Jianguo1 ; Pei, Donghe2
1 School of Science, China University of Petroleum (east China), Qingdao, 266555, P. R. China
2 School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 3, p. 275-284.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.008.03.12
Classification : 51B20, 53B50, 53A35
Keywords: Null Bertrand curve, AW(k)-type curve, Frenet frame, null cone.

Sun, Jianguo 1 ; Pei, Donghe 2

1 School of Science, China University of Petroleum (east China), Qingdao, 266555, P. R. China
2 School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China 
@article{JNSA_2015_8_3_a11,
     author = {Sun, Jianguo and Pei, Donghe},
     title = {Some new properties of null curves on 3-null cone and unit {semi-Euclidean} 3-spheres},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {275-284},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2015},
     doi = {10.22436/jnsa.008.03.12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.03.12/}
}
TY  - JOUR
AU  - Sun, Jianguo
AU  - Pei, Donghe
TI  - Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres
JO  - Journal of nonlinear sciences and its applications
PY  - 2015
SP  - 275
EP  - 284
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.03.12/
DO  - 10.22436/jnsa.008.03.12
LA  - en
ID  - JNSA_2015_8_3_a11
ER  - 
%0 Journal Article
%A Sun, Jianguo
%A Pei, Donghe
%T Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres
%J Journal of nonlinear sciences and its applications
%D 2015
%P 275-284
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.03.12/
%R 10.22436/jnsa.008.03.12
%G en
%F JNSA_2015_8_3_a11
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 its applications, Tome 8 (2015) no. 3, p. 275-284. doi : 10.22436/jnsa.008.03.12. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.03.12/

[1] Arslan, K.; 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] Balgetir, H.; Bektaş, M.; M. Ergüt Bertrand cuves for nonnull curves in 3 dimensional Lorentzian space , Hadronic Journal, Volume 27 (2004), pp. 229-236

[3] Balgetir, H.; Bektaş, M.; Inoguchi, J. Null Bertrand curves in Minkowski 3 space and their characterizations, Note di Matematica, Volume 23 (2004), pp. 7-13

[4] Barros, M.; Ferrández, A. Null scrolls as solutions of a sigma model, J. Phys. A-Math. thoer., Volume 45 (2012), pp. 1-12

[5] Campanelli, M.; Lousto, C. O. Second order gauge invariant gravitational perturbations of a Kerr black hole, Phys. Rev. D, Volume 59 (1999), pp. 1-16

[6] Duggal, K. L.; D. H. Jin Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, , 2007

[7] Ersoy, S.; Inalcik, A. On the generalized timelike Bertrand curves in 5-dimensional Lorentzian space, Differential Geom.-Dynamical Systems, Volume 13 (2011), pp. 78-88

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

[9] Göçmen, M.; Keleş, S. arXiv preprint , arXiv:1104.3230 , 2011

[10] Ilarslan, K.; Boyacıoğlu, Ö. Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos Solitons Fractals, Volume 38 (2008), pp. 1383-1389

[11] Kong, L. L.; D. H. Pei On spacelike curves in hyperbolic space times sphere, Int. J. Geom. Methods Mod. Phys., Volume 11 (2014), pp. 1-12

[12] Kozameh, C.; Lamberti, P. W.; Reula, O. Global aspects of light cone cuts, J. Math. Phys., Volume 32 (1991), pp. 3423-3426

[13] Külahcı, M.; M. Ergüt Bertrand curves of AW(k)-type in Lorentzian space, Nonlinear Anal., Volume 70 (2009), pp. 1725-1731

[14] Külahcı, M.; Bektaş, M.; M. Ergüt Curves of AW(k)-type in 3-dimensional null cone, Phys. Lett. A, Volume 371 (2007), pp. 275-277

[15] Lucas, P.; Ortega-Yagües, J. A. Bertrand curves in the three-dimensional sphere, J. Geom. Phys., Volume 62 (2012), pp. 1903-1914

[16] B. O’Neill Semi-Riemannian Geomerty with applications to relativity, Academic press, London, 1983

[17] Neraessian, A.; Ramos, E. Massive spinning particles and the geometry of null curves, Phys. Lett. B, Volume 445 (1998), pp. 123-128

[18] Özgür, C.; Gezgin, F. On some curves of AW(k)-type, Differential Geom.-Dynamical systems, Volume 7 (2005), pp. 74-80

[19] Oztekin, H. B. Weakened Bertrand curves in the Galilean space G3, J. Adv. Math. Studies, Volume 2 (2009), pp. 69-76

[20] Pears, L. R. Bertrand curves in Riemannian space, J. London Math. Soc., Volume 1 (1935), pp. 180-183

[21] Papaioannou, S. G.; D. Kiritsis An application of Bertrand curves and surfaces to CADCAM , Comput. Aided Geom. Design, Volume 17 (1985), pp. 348-352

[22] Penrose, R. A. Remarkable property of plane waves in general relativity, Rev. Modern Phys., Volume 37 (1965), pp. 215-220

[23] Sun, J. G.; Pei, D. H. Null Cartan Bertrand curves of AW(k)-type in Minkowski 4-space, Phys. Lett. A, Volume 376 (2012), pp. 2230-2233

[24] Sun, J. G.; Pei, D. H. Families of Gauss indicatrices on Lorentzian hypersurfaces in pseudo-spheres in semi- Euclidean 4 space, J. Math. Anal. Appl., Volume 400 (2013), pp. 133-142

[25] Sun, J. G.; Pei, D. H. Null surfaces of null curves on 3-null cone, Phys. Lett. A, Volume 378 (2014), pp. 1010-1016

[26] Tian, G. H.; Zhao, Z.; Liang, C. B. Proper acceleration' of a null geodesic in curved spacetime, Classical Quant. Grav., Volume 20 (2003), pp. 1-4329

[27] Yilmaz, M. Y.; Bektaş, M. General properties of Bertrand curves in Riemann-Otsuki space, Nonlinear Anal., Volume 69 (2008), pp. 3225-3231

Cité par Sources :