On canonical screen for lightlike submanifolds of codimension two
Abstract
In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.
-
[1] M.A. Akivis and V.V. Goldberg: “On some methods of construction of invariant normalizations of lightlike hypersurfaces”, Differential Geom. Appl., Vol. 12, (2000), pp. 121–143. http://dx.doi.org/10.1016/S0926-2245(00)00008-5
-
[2] C. Atindogbe and K.L. Duggal: “Conformal screen on lightlike hypersurfaces”, Int. J. Pure Appl. Math., Vol. 11, (2004), pp. 421–442.
-
[3] J.K. Beem and P.E. Ehrlich: Global Lorentzian geometry, Monographs and Textbooks in Pure and Applied Math., Vol. 67, Marcel Dekker, New York, 1981.
-
[4] K.L. Duggal: “On scalar curvature in lightlike geometry”, J. Geom. Phys., Vol. 57, (2007), pp. 473–481. http://dx.doi.org/10.1016/j.geomphys.2006.04.001
-
[5] K.L. Duggal: “A report on canonical null curves and screen distributions for lightlike geometry”, Acta Appl. Math., Vol. 95, (2007), pp. 135–149. http://dx.doi.org/10.1007/s10440-006-9082-x
-
[6] K.L. Duggal and A. Bejancu: “Lightlike submanifolds of codimension two”, Math. J. Toyama Univ., Vol. 15, (1992), pp. 59–82.
-
[7] K.L. Duggal and A. Bejancu: Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and its Applications, Vol. 364, Kluwer Academic Publishers Group, Dordrecht, 1996.
-
[8] K.L. Duggal and D.H. Jin: “Half lightlike submanifolds of codimension 2”, Math. J. Toyama Univ., Vol. 22, (1999), pp. 121–161.
-
[9] K.L. Duggal and B. Sahin: “Screen conformal half-lightlike submanifolds”, Int. J. Math. Math. Sci., Vol. 68, (2004), pp. 3737–3753. http://dx.doi.org/10.1155/S0161171204403342
-
[10] K.L. Duggal and A. Giménez: “Lightlike hypersurfaces of Lorentzian manifolds with distinguished screen”, J. Geom. Phys., Vol. 55, (2005), pp. 107–122. http://dx.doi.org/10.1016/j.geomphys.2004.12.004
-
[11] D.H. Jin: “Geometry of coisotropic submanifolds”, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math., Vol. 8, no. 1, (2001), pp. 33–46.
-
[12] B. O’Neill: Semi-Riemannian geometry with applications to relativity, Pure and Applied Mathematics, Vol. 103, Academic Press, New York, 1983.
