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Year 2013, Volume: 6 Issue: 2, 70 - 78, 30.10.2013

Wenjie Wang , Ximin Lıu

Abstract

References

  • [1] Deprez, J., Semi-parallel surfaces in Euclidean space, J. Geom., 25 (1985), 192-200.
  • [2] Duggal, K.L. and Bejancu, A., Lightlike submanifolds of codimensional two, Math. J. Toyama Univ., 15 (1992), 59-82.
  • [3] Duggal, K.L. and Bejancu, A., Lightlike submainfolds of semi-Riemannian mainfolds and applications, Kluer Academic Publishers, Dordrecht, 1996.
  • [4] Duggal, K.L. and Jin, D.H., Half lightlike submanifolds of codimensional 2, Math. J. Toyama Univ., 22 (1999), 121-161.
  • [5] Duggal, K.L. and Jin, D.H., Null curves and hypersurfaces of semi-Riemannian manifolds, World Scientific, Hackensack NJ, 2007.
  • [6] Duggal, K.L. and Sahin, B., Differential geometry of lightlike submanifolds, Birkh¨auser Ver- alag AG, Basel, Boston, Berlin, 2010.
  • [7] Ferus, D.,Immersions with parallel second fundamental form, Math. Z., 140 (1974), 93-103.
  • [8] Jin, D.H., Special half lightlike submanifolds of an indefinite Sasakian manifolds, to appear.
  • [9] Jin, D.H., Special half lightlike submanifolds of an indefinite cosymplectic manifolds, J. Funct. Spaces Appl., Volume 2012, Article ID 632624, 16 pages.
  • [10] Jin, D.H. and Lee, J.W., Generic lightlike submanifolds of an indefinite cosymplectic mani- folds, Math. Probl. Eng., Volume 2011, Article ID 610986, 16 pages.
  • [11] Kupeli, D.N., Singular semi-Riemnnian Geometry, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  • [12] Massamba, F., Semi-Parallel lightlike hypersurfaces of indefinite Sasakian manifolds, Int. J. Contemp. Math. Sci., 3 (2008), 629-634.
  • [13] Massamba, F., Lightlike hypersurfaces of indefinite Sasakian manifolds with parallel symmet- ric bilinear forms, Differ. Geom. Dyn. Syst., 10 (2008), 226-234.
  • [14] Massamba, F., On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds, J. Geom., 95 (2009), 73-89.
  • [15] Upadhyay, A. and Gupta, R.S., Semi-parallel lightlike hypersurfaces of indefinite cosymplectic space forms, Publ. Inst. Math. (Beograd) (N.S.), 89 (2011), 69-75.
  • [16] Wang, W.J. and Liu, X.M., On Parallelism of half-Lightlike submanifolds of indefinite Ken- motsu manifolds, Geom., Volume 2013, Article ID 615819, 6 pages.

ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS

Year 2013, Volume: 6 Issue: 2, 70 - 78, 30.10.2013

Wenjie Wang , Ximin Lıu

Abstract




Keywords

Ascreen half lightlike submanifold indefinite cosymplectic manifold semi-parallel parallel second fundamental form

References

  • [1] Deprez, J., Semi-parallel surfaces in Euclidean space, J. Geom., 25 (1985), 192-200.
  • [2] Duggal, K.L. and Bejancu, A., Lightlike submanifolds of codimensional two, Math. J. Toyama Univ., 15 (1992), 59-82.
  • [3] Duggal, K.L. and Bejancu, A., Lightlike submainfolds of semi-Riemannian mainfolds and applications, Kluer Academic Publishers, Dordrecht, 1996.
  • [4] Duggal, K.L. and Jin, D.H., Half lightlike submanifolds of codimensional 2, Math. J. Toyama Univ., 22 (1999), 121-161.
  • [5] Duggal, K.L. and Jin, D.H., Null curves and hypersurfaces of semi-Riemannian manifolds, World Scientific, Hackensack NJ, 2007.
  • [6] Duggal, K.L. and Sahin, B., Differential geometry of lightlike submanifolds, Birkh¨auser Ver- alag AG, Basel, Boston, Berlin, 2010.
  • [7] Ferus, D.,Immersions with parallel second fundamental form, Math. Z., 140 (1974), 93-103.
  • [8] Jin, D.H., Special half lightlike submanifolds of an indefinite Sasakian manifolds, to appear.
  • [9] Jin, D.H., Special half lightlike submanifolds of an indefinite cosymplectic manifolds, J. Funct. Spaces Appl., Volume 2012, Article ID 632624, 16 pages.
  • [10] Jin, D.H. and Lee, J.W., Generic lightlike submanifolds of an indefinite cosymplectic mani- folds, Math. Probl. Eng., Volume 2011, Article ID 610986, 16 pages.
  • [11] Kupeli, D.N., Singular semi-Riemnnian Geometry, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  • [12] Massamba, F., Semi-Parallel lightlike hypersurfaces of indefinite Sasakian manifolds, Int. J. Contemp. Math. Sci., 3 (2008), 629-634.
  • [13] Massamba, F., Lightlike hypersurfaces of indefinite Sasakian manifolds with parallel symmet- ric bilinear forms, Differ. Geom. Dyn. Syst., 10 (2008), 226-234.
  • [14] Massamba, F., On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds, J. Geom., 95 (2009), 73-89.
  • [15] Upadhyay, A. and Gupta, R.S., Semi-parallel lightlike hypersurfaces of indefinite cosymplectic space forms, Publ. Inst. Math. (Beograd) (N.S.), 89 (2011), 69-75.
  • [16] Wang, W.J. and Liu, X.M., On Parallelism of half-Lightlike submanifolds of indefinite Ken- motsu manifolds, Geom., Volume 2013, Article ID 615819, 6 pages.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Wenjie Wang

Ximin Lıu

Publication Date October 30, 2013
Published in Issue Year 2013 Volume: 6 Issue: 2

Cite

APA Wang, W., & Lıu, X. (2013). ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS. International Electronic Journal of Geometry, 6(2), 70-78.
AMA Wang W, Lıu X. ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS. Int. Electron. J. Geom. October 2013;6(2):70-78.
Chicago Wang, Wenjie, and Ximin Lıu. “ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS”. International Electronic Journal of Geometry 6, no. 2 (October 2013): 70-78.
EndNote Wang W, Lıu X (October 1, 2013) ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS. International Electronic Journal of Geometry 6 2 70–78.
IEEE W. Wang and X. Lıu, “ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS”, Int. Electron. J. Geom., vol. 6, no. 2, pp. 70–78, 2013.
ISNAD Wang, Wenjie - Lıu, Ximin. “ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS”. International Electronic Journal of Geometry 6/2 (October 2013), 70-78.
JAMA Wang W, Lıu X. ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS. Int. Electron. J. Geom. 2013;6:70–78.
MLA Wang, Wenjie and Ximin Lıu. “ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS”. International Electronic Journal of Geometry, vol. 6, no. 2, 2013, pp. 70-78.
Vancouver Wang W, Lıu X. ON PARALLELISM OF ASCREEN HALF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE COSYMPLECTIC MANIFOLDS. Int. Electron. J. Geom. 2013;6(2):70-8.