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GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

Yıl 2012, Cilt: 5 Sayı: 1, 108 - 119, 30.04.2012

Öz


Kaynakça

  • [1] De Rham, G. Sur la r´eductibilit´e d’un espace de Riemannian, Comm. Math. Helv. 26(1952), 328–344.
  • [2] Duggal, K. L. Spacetime manifolds and contact structures, Int. J. Math. & Math. Sci., 13,(1990), 545–554.
  • [3] Duggal, K. L. and Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  • [4] Duggal, K. L. and Jin, D. H . Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  • [5] Duggal, K. L. and Sahin, B. Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkh¨auser, 2010.
  • [6] Duggal, K. L. and Jin, D. H., Totally umbilical lightlike submanifolds, Kodai Math. J. vol. 26(2003), 49-68.
  • [7] Hawking, S.W. and Ellis, G.F.R . The large scale structure of space-time, Cambridge Uni- versity Press, Cambridge, 1973.
  • [8] Jin, D. H. Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold, Indian J. of Pure and Applied Math., 41(1)(2010), 569–581.
  • [9] Jin, D. H. Transversal half lightlike submanifolds of an indefinite Sasakian manifold, J. Korean Soc Math. Edu. Ser. B: Pure Appl. Math., 18(1)(2011), 51–61.
  • [10] Jin, D. H. Half lightlike submanifold of an indefinite Sasakian manifold, J. Korean Soc Math. Edu. Ser. B: Pure Appl. Math., 18(2)(2011), 173–183.
  • [11] Jin, D. H. and Lee, J. W. Generic lightlike submanifolds of an indefinite cosymplectic mani- fold, Mathematical Problems in Engineering, Article ID 610986,(2011), 16 pages.
  • [12] Kupeli, D. N. Singular Semi-Riemannian Geometry, Mathematics and Its Applications, vol. 366, Kluwer Acad. Publishers, Dordrecht, 1996.
  • [13] O’Neill, B. Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.
  • [14] Yano, K. and Kon, M. Generic submanifolds, Ann. di Math. pura Appl., 123(1980), 59–92. [15] Yano, K. and Kon, M. Generic submanifolds of Sasakian manifolds, Kodai Math. J., 3(1980), 163–196.
Yıl 2012, Cilt: 5 Sayı: 1, 108 - 119, 30.04.2012

Öz

Kaynakça

  • [1] De Rham, G. Sur la r´eductibilit´e d’un espace de Riemannian, Comm. Math. Helv. 26(1952), 328–344.
  • [2] Duggal, K. L. Spacetime manifolds and contact structures, Int. J. Math. & Math. Sci., 13,(1990), 545–554.
  • [3] Duggal, K. L. and Bejancu, A. Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  • [4] Duggal, K. L. and Jin, D. H . Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  • [5] Duggal, K. L. and Sahin, B. Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkh¨auser, 2010.
  • [6] Duggal, K. L. and Jin, D. H., Totally umbilical lightlike submanifolds, Kodai Math. J. vol. 26(2003), 49-68.
  • [7] Hawking, S.W. and Ellis, G.F.R . The large scale structure of space-time, Cambridge Uni- versity Press, Cambridge, 1973.
  • [8] Jin, D. H. Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold, Indian J. of Pure and Applied Math., 41(1)(2010), 569–581.
  • [9] Jin, D. H. Transversal half lightlike submanifolds of an indefinite Sasakian manifold, J. Korean Soc Math. Edu. Ser. B: Pure Appl. Math., 18(1)(2011), 51–61.
  • [10] Jin, D. H. Half lightlike submanifold of an indefinite Sasakian manifold, J. Korean Soc Math. Edu. Ser. B: Pure Appl. Math., 18(2)(2011), 173–183.
  • [11] Jin, D. H. and Lee, J. W. Generic lightlike submanifolds of an indefinite cosymplectic mani- fold, Mathematical Problems in Engineering, Article ID 610986,(2011), 16 pages.
  • [12] Kupeli, D. N. Singular Semi-Riemannian Geometry, Mathematics and Its Applications, vol. 366, Kluwer Acad. Publishers, Dordrecht, 1996.
  • [13] O’Neill, B. Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.
  • [14] Yano, K. and Kon, M. Generic submanifolds, Ann. di Math. pura Appl., 123(1980), 59–92. [15] Yano, K. and Kon, M. Generic submanifolds of Sasakian manifolds, Kodai Math. J., 3(1980), 163–196.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

K.l. Duggal

D. J. Jın Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2012
Yayımlandığı Sayı Yıl 2012 Cilt: 5 Sayı: 1

Kaynak Göster

APA Duggal, K., & Jın, D. J. (2012). GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD. International Electronic Journal of Geometry, 5(1), 108-119.
AMA Duggal K, Jın DJ. GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD. Int. Electron. J. Geom. Nisan 2012;5(1):108-119.
Chicago Duggal, K.l., ve D. J. Jın. “GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD”. International Electronic Journal of Geometry 5, sy. 1 (Nisan 2012): 108-19.
EndNote Duggal K, Jın DJ (01 Nisan 2012) GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD. International Electronic Journal of Geometry 5 1 108–119.
IEEE K. Duggal ve D. J. Jın, “GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD”, Int. Electron. J. Geom., c. 5, sy. 1, ss. 108–119, 2012.
ISNAD Duggal, K.l. - Jın, D. J. “GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD”. International Electronic Journal of Geometry 5/1 (Nisan 2012), 108-119.
JAMA Duggal K, Jın DJ. GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD. Int. Electron. J. Geom. 2012;5:108–119.
MLA Duggal, K.l. ve D. J. Jın. “GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD”. International Electronic Journal of Geometry, c. 5, sy. 1, 2012, ss. 108-19.
Vancouver Duggal K, Jın DJ. GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD. Int. Electron. J. Geom. 2012;5(1):108-19.