On canonical screen for lightlike submanifolds of codimension two

K. Duggal 1
  • 1 University of Windsor


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.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [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.


Journal + Issues

Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant and original works in all areas of mathematics. The journal publishes both research papers and comprehensive and timely survey articles. Open Math aims at presenting high-impact and relevant research on topics across the full span of mathematics.