Research Article
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Year 2008, Volume 1, Issue 1, 25 - 32, 30.04.2008

Abstract

References

  • [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.

On existence of canonical screens for coisotropic submanifolds

Year 2008, Volume 1, Issue 1, 25 - 32, 30.04.2008

Abstract

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.

References

  • [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.

Details

Primary Language English
Subjects Mathematics
Journal Section Research Article
Authors

Krishan L. DUGGAL>

Publication Date April 30, 2008
Published in Issue Year 2008, Volume 1, Issue 1

Cite

Bibtex @research article { iejg581489, journal = {International Electronic Journal of Geometry}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2008}, volume = {1}, number = {1}, pages = {25 - 32}, title = {On existence of canonical screens for coisotropic submanifolds}, key = {cite}, author = {Duggal, Krishan L.} }
APA Duggal, K. L. (2008). On existence of canonical screens for coisotropic submanifolds . International Electronic Journal of Geometry , 1 (1) , 25-32 . Retrieved from https://dergipark.org.tr/en/pub/iejg/issue/46277/581489
MLA Duggal, K. L. "On existence of canonical screens for coisotropic submanifolds" . International Electronic Journal of Geometry 1 (2008 ): 25-32 <https://dergipark.org.tr/en/pub/iejg/issue/46277/581489>
Chicago Duggal, K. L. "On existence of canonical screens for coisotropic submanifolds". International Electronic Journal of Geometry 1 (2008 ): 25-32
RIS TY - JOUR T1 - On existence of canonical screens for coisotropic submanifolds AU - Krishan L.Duggal Y1 - 2008 PY - 2008 N1 - DO - T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 25 EP - 32 VL - 1 IS - 1 SN - -1307-5624 M3 - UR - Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Geometry On existence of canonical screens for coisotropic submanifolds %A Krishan L. Duggal %T On existence of canonical screens for coisotropic submanifolds %D 2008 %J International Electronic Journal of Geometry %P -1307-5624 %V 1 %N 1 %R %U
ISNAD Duggal, Krishan L. . "On existence of canonical screens for coisotropic submanifolds". International Electronic Journal of Geometry 1 / 1 (April 2008): 25-32 .
AMA Duggal K. L. On existence of canonical screens for coisotropic submanifolds. Int. Electron. J. Geom.. 2008; 1(1): 25-32.
Vancouver Duggal K. L. On existence of canonical screens for coisotropic submanifolds. International Electronic Journal of Geometry. 2008; 1(1): 25-32.
IEEE K. L. Duggal , "On existence of canonical screens for coisotropic submanifolds", International Electronic Journal of Geometry, vol. 1, no. 1, pp. 25-32, Apr. 2008