Singularities of dual hypersurfaces of spacelike hypersurfaces in lightcone and Legendrian duality
-
1698
Downloads
-
2684
Views
Authors
Meiling He
- School of Mathematical Sciences, Harbin Normal University, Harbin, 150500, P. R. China.
Yang Jiang
- College of Maths and Systematic Science, Shenyang Normal University, Shenyang, 110034, P. R. China.
Zhigang Wang
- School of Mathematical Sciences, Harbin Normal University, Harbin, 150500, P. R. China.
Abstract
The theory of the Legendrian singularity is applied for lightcones that are canonically embedded in the
higher-dimensional lightcone and de Sitter space in the Minkowski space-time. The singularities of two
classes of hypersurfaces that are dual to space-like hypersurface in the lightcone under Legendrian dualities
are analyzed in detail.
Share and Cite
ISRP Style
Meiling He, Yang Jiang, Zhigang Wang, Singularities of dual hypersurfaces of spacelike hypersurfaces in lightcone and Legendrian duality, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 9, 5471--5487
AMA Style
He Meiling, Jiang Yang, Wang Zhigang, Singularities of dual hypersurfaces of spacelike hypersurfaces in lightcone and Legendrian duality. J. Nonlinear Sci. Appl. (2016); 9(9):5471--5487
Chicago/Turabian Style
He, Meiling, Jiang, Yang, Wang, Zhigang. "Singularities of dual hypersurfaces of spacelike hypersurfaces in lightcone and Legendrian duality." Journal of Nonlinear Sciences and Applications, 9, no. 9 (2016): 5471--5487
Keywords
- Singularity
- Legendrian duality
- light-cone frame.
MSC
References
-
[1]
V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, Vol. I, The classification of critical points, caustics and wave fronts, Translated from the Russian by Ian Porteous and Mark Reynolds, Monographs in Mathematics, Birkhäuser Boston, Inc., Boston (1985)
-
[2]
A. C. Asperti, M. Dajczer, Conformally at Riemannian manifolds as hypersurfaces of the light cone, Canad. Math. Bull., 32 (1989), 281--285
-
[3]
S. J. Brodsky, H. C. Pauli, S. S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rep., 301 (1998), 299--486
-
[4]
S. Izumiya, Lengendrian dualities and spacelike hypersurfaces in the lightcone, Mosc. Math. J., 9 (2009), 325--357
-
[5]
S. Izumiya, Y. Jiang, D. H. Pei, Lightcone dualities for curves in the sphere, Q. J. Math., 64 (2013), 221--234
-
[6]
S. Izumiya, Y. Jiang, D. H. Pei, Lightcone dualities for hypersurfaces in the sphere, Math. Nachr., 287 (2014), 1687--1700
-
[7]
S. Izumiya, Y. Jiang, T. Sato, Lightcone dualities for curves in the lightcone unit 3-sphere, Math. Phys., 54 (2013), 15 pages
-
[8]
M. Kasedou, Spacelike submanifolds of codimension two in de Sitter space, J. Geom. Phys., 60 (2010), 31--42
-
[9]
J. Martinet, Singularities of smooth functions and maps, Translated from the French by Carl P. Simon, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge-New York (1982)
-
[10]
R. R. Metsaev, C. B. Thorn, A. A. Tseytlin, Light-cone superstring in AdS space-time, Nuclear Phys. B, 596 (2001), 151--184
-
[11]
J. A. Montaldi, On contact between submanifolds, Michigan Math. J., 33 (1986), 191--195
-
[12]
Z. G. Wang, D. H. Pei, Singularities of ruled null surfaces of the principal normal indicatrix to a null Cartan curve in de Sitter 3-space, Phys. Lett. B, 689 (2010), 101--106
-
[13]
Z. G. Wang, D. H. Pei, Null Darboux developable and pseudo-spherical Darboux image of null Cartan curve in Minkowski 3-space, Hokkaido Math. J., 40 (2011), 219--240
-
[14]
Z. G. Wang, D. H. Pei, L. Chen, Geometry of 1-lightlike submanifolds in antide Sitter n-space, Proc. Roy. Soc. Edinburgh Sect. A, 143 (2013), 1089--1113
-
[15]
Z. G. Wang, D. H. Pei, X. M. Fan, Singularities of null developable of timelike curve that lies on nullcone in semi-Euclidean 3-space with index 2, Topology Appl., 160 (2013), 189--198
-
[16]
Z. G. Wang, D. H. Pei, L. L. Kong, Gaussian surfaces and nullcone dual surfaces of null curves in a three- dimensional nullcone with index 2, J. Geom. Phys, 73 (2013), 166--86
-
[17]
G. Wassermann, Stability of caustics, Math. Ann., 216 (1975), 43--50
-
[18]
V. M. Zakalyukin, Lagrangian and Legendrian singularities, Funct. Anal. Appl., 10 (1976), 23--31