Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GCR-LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN PRODUCT MANIFOLD

  • Received : 2013.05.23
  • Published : 2014.05.31
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Abstract

We introduce GCR-lightlike submanifold of a semi-Riemannian product manifold and give an example. We study geodesic GCR-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product. Finally, we discuss minimal GCR-lightlike submanifolds of a semi-Riemannian product manifold.

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References

  1. M. Atceken and E. Kilic, Semi-invariant lightlike submanifolds of a semi-Riemannian product manifold, Kodai Math. J. 30 (2007), no. 3, 361-378. https://doi.org/10.2996/kmj/1193924940
  2. C. L. Bejan and K. L. Duggal, Global lightlike manifolds and harmonicity, Kodai Math. J. 28 (2005), no. 1, 131-145. https://doi.org/10.2996/kmj/1111588042
  3. K. L. Duggal, CR-structures and Lorentzian geometry, Acta Appl. Math. 7 (1986), no. 3, 211-223. https://doi.org/10.1007/BF00047093
  4. K. L. Duggal, Lorentzian geometry of CR submanifolds, Acta Appl. Math. 17 (1989), no. 2, 171-193. https://doi.org/10.1007/BF00046823
  5. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of semi-Riemannian Manifolds and Applications, Vol. 364 of Mathematics and its Applications, Kluwer Academic Publishers, The Netherlands, 1996.
  6. K. L. Duggal and D. H. Jin, Totally umbilical lightlike submanifolds, Kodai Math. J. 26 (2003), no. 1, 49-68. https://doi.org/10.2996/kmj/1050496648
  7. K. L. Duggal and B. Sahin, Screen Cauchy-Riemann lightlike submanifolds, Acta Math. Hungar. 106 (2005), no. 1-2, 137-165. https://doi.org/10.1007/s10474-005-0011-7
  8. K. L. Duggal and B. Sahin, Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hungar. 112 (2006), no. 1-2, 107-130. https://doi.org/10.1007/s10474-006-0068-y
  9. S. M. Khursheed Haider, Mamta Thakur, and Advin, Screen Cauchy-Riemann lightlike submanifolds of a semi-Riemannian product manifold, Int. Electron. J. Geom. 4 (2011), no. 2, 141-154.
  10. E. Kilic, B. Sahin, and S. Keles, Screen semi invariant lightlike submanifolds of a semi-Riemannian product manifolds, Int. Electron. J. Geom. 4 (2011), 120-135.
  11. R. Kumar, S. Kumar, and R. K. Nagaich, GCR-lightlike product of indefinite Kaehler manifolds, ISRN Geometry. 2011 (2011), Article ID 531281, 13 pages.
  12. R. Kumar, S. Kumar, and R. K. Nagaich, Integrability of distributions in GCR-lightlike submanifolds of indefinite Kaehler manifolds, Commun. Korean Math. Soc. 27 (2012), no. 3, 591-602. https://doi.org/10.4134/CKMS.2012.27.3.591
  13. S. Kumar, R. Kumar, and R. K. Nagaich, Characterization of holomorphic bisectional curvature of GCR-lightlike submanifolds, Advances in Mathematical Physics. 2012 (2012), Article ID 356263, 18 pages.
  14. S. Kumar, R. Kumar, and R. K. Nagaich, GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds, Bull. Korean Math. Soc. 50 (2013), no. 4, 1173-1192. https://doi.org/10.4134/BKMS.2013.50.4.1173
  15. D. N. Kupeli, Singular Semi-Riemannian Geometry, vol. 366, Kluwer, Dordrecht, 1996.
  16. B. O'Neill, Semi-Riemannian Geometry with Applicitaions to Relativity, Academic Press, New York, 1983.
  17. B. Sahin and M. Atceken, Semi-Invariant submanifolds of Riemannian product manifold, Balkan J. Geom. Appl. 8 (2003), no. 1, 91-100.
  18. X. Senlin and N. Yilong, Submanifolds of product Riemannian manifold, Acta Math. Sci. Ser. B Engl. Ed. 20 (2000), no. 2, 213-218.

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