On existence of canonical screens for coisotropic submanifolds

Yıl 2008, Cilt: 1 Sayı: 1, 25 - 32, 30.04.2008

Krishan L. Duggal

Öz

In this paper we study coisotropic lightlike submanifolds of a semi-Riemannian manifold. For a large variety of this class of submanifolds, we
prove two theorems on the existence of integrable canonical screen distribution
and canonical null transversal bundle subject to some reasonable geometric
conditions.

Anahtar Kelimeler

coisotropic submanifold, canonical screen distribution, screen transformation equations, null transversal bundle

Kaynakça

• [1] Akivis, M. A. and Goldberg, V. V., On some methods of construction of invariant normalizations of lightlike hypersurfaces, Differential Geometry and its Applications, 12(2000), no.2, 121-143.
• [2] Bejancu, A., A canonical screen distribution on a degenerate hypersurface, Scientific Bulletin, Series A, Applied Math. and Physics, 55(1993), 55-61.
• [3] Bejancu, A. and Duggal, K. L., Degenerate hypersurfaces of semi-Riemannian manifolds, Bull. Inst. Politehnie Iasi, (S.1), 37(1991), 13-22.
• [4] Bejancu, A., Ferrandez, A. and Lucas P., A new viewpoint on geometry of a lightlike hyper- surface in a semi-Euclidean space, Saitama Math. J., (1998), 31-38.
• [5] Bonnor, W. B., Null hypersurfaces in Minkowski spacetime, Tensor (N.S.), 24(1972), 329-245.
• [6] Duggal, K. L., On scalar curvature in lightlike geometry, J. Geom. Phys., 57(2007), 473-481.
• [7] Duggal, K. L., A Report on Canonical Null Curves and Screen Distributions for Lightlike Geometry, Acta Appli Math., 95(2007), 135-149.
• [8] Duggal, K. L., On canonical screen for lightlike submanifolds of codimension two. Central European Journal of Mathematics, CEJM, 5(4)(2007), 710-719.
• [9] Duggal, K. L., Bejancu, A., Lightlike submanifolds of semi-Riemannian manifolds and appli- cations, Kluwer, Dordrecht, 364, 1996.
• [10] IIyenko, K., Twistor representation of null 2-surfaces, J. Math. Phys., 10(2002), 4770-4789.
• [11] Israel, W., Event horizons in static vacuum spacetimes, Phys. Rev., 164(1967), 1776-1779.
• [12] Israel, W., Event horizons in static electrovac spacetimes, Comm. Math. Phys., 8(1968), 245-260.
• [13] Jin, D. H., Geometry of coisotropic submanifolds, , J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math.,8(2001), no. 1, 33-46.
• [14] Katsuno, K., Null hypersurfaces in Lorentzian manifolds, Math. Proc. Cab. Phil. Soc., 88(1980), 175-182.
• [15] Leistner, T., Screen bundles of Lorentzian manifolds and some generalizations of pp-waves, J. Geom. Phys., 56(2006), no. 10, 2117-2134.
• [16] Nurowski, P. and Robinsom, D., Intrinsic geometry of a null hypersurface, Class. Quantum Grav., 17(2000), 4065-4084.
• [17] O'Neill, B., Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983.
• [18] Penrose, R., The twistor geometry of light rays. Geometry and physics, Classical Quantum Gravity, 14(1A), 1997, A299-A323.
• [19] Perlick, V., On totally umbilical submanifolds of semi-Riemannian manifolds, Nonlinear Anal- ysis, 63(2005), 511-518.
• [20] Rosca, R., On null hypersurfaces of a Lorentzian manifold, Tensor (N.S.), 23(1972), 66-74.