On canonical screen for lightlike submanifolds of codimension two

K. Duggal

Open Mathematics (2007)

  • Volume: 5, Issue: 4, page 710-719
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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K. Duggal. "On canonical screen for lightlike submanifolds of codimension two." Open Mathematics 5.4 (2007): 710-719. <http://eudml.org/doc/269609>.

@article{K2007,
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.},
author = {K. Duggal},
journal = {Open Mathematics},
keywords = {Half lightlike submanifold; coisotropic submanifold; canonical screen distribution; screen conformal fundamental forms; half light-like submanifold},
language = {eng},
number = {4},
pages = {710-719},
title = {On canonical screen for lightlike submanifolds of codimension two},
url = {http://eudml.org/doc/269609},
volume = {5},
year = {2007},
}

TY - JOUR
AU - K. Duggal
TI - On canonical screen for lightlike submanifolds of codimension two
JO - Open Mathematics
PY - 2007
VL - 5
IS - 4
SP - 710
EP - 719
AB - 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.
LA - eng
KW - Half lightlike submanifold; coisotropic submanifold; canonical screen distribution; screen conformal fundamental forms; half light-like submanifold
UR - http://eudml.org/doc/269609
ER -

References

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  1. [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 Zbl0965.53022
  2. [2] C. Atindogbe and K.L. Duggal: “Conformal screen on lightlike hypersurfaces”, Int. J. Pure Appl. Math., Vol. 11, (2004), pp. 421–442. Zbl1057.53051
  3. [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. [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 Zbl1107.53047
  5. [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 Zbl1117.53019
  6. [6] K.L. Duggal and A. Bejancu: “Lightlike submanifolds of codimension two”, Math. J. Toyama Univ., Vol. 15, (1992), pp. 59–82. Zbl0777.53020
  7. [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. Zbl0848.53001
  8. [8] K.L. Duggal and D.H. Jin: “Half lightlike submanifolds of codimension 2”, Math. J. Toyama Univ., Vol. 22, (1999), pp. 121–161. Zbl0995.53051
  9. [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 Zbl1071.53041
  10. [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 Zbl1111.53029
  11. [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. Zbl1203.53047
  12. [12] B. O’Neill: Semi-Riemannian geometry with applications to relativity, Pure and Applied Mathematics, Vol. 103, Academic Press, New York, 1983. 

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