Bulletin of the Korean Mathematical Society (대한수학회보)

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HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD

  • Jin, Dae Ho (Department of Mathematics Dongguk University)
  • Received : 2013.07.16
  • Published : 2014.07.31
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Abstract

We study half lightlike submanifold M of an indefinite trans-Sasakian manifold such that its structure vector field is tangent to M. First we study the general theory for such half lightlike submanifolds. Next we prove some characterization theorems for half lightlike submanifolds of an indefinite generalized Sasakian space form.

Keywords

References

  1. R. Al-Ghefari, F. R. Al-Solamy, and M. H. Shahid, Contact CR-warped product sub-manifolds in generalized Sasakian space forms, Balkan J. Geom. Appl. 11 (2006), no. 2, 1-10.
  2. P. Alegre, D. E. Blair, and A. Carriazo, Generalized Sasakian space form, Israel J. Math. 141 (2004), 157-183. https://doi.org/10.1007/BF02772217
  3. C. Calin, Contributions to geometry of CR-submanifold, Thesis, University of Iasi, Romania, 1998.
  4. G. de Rham, Sur la reductibilite d'un espace de Riemannian, Comm. Math. Helv. 26 (1952), 328-344. https://doi.org/10.1007/BF02564308
  5. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  6. K. L. Duggal and D. H. Jin, Half-lightlike submanifolds of codimension 2, Math. J. Toyama Univ. 22 (1999), 121-161.
  7. K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  8. K. L. Duggal and D. H. Jin, Generic lightlike submanifolds of an indefinite Sasakian manifold, Int. Electron. J. Geom. 5 (2012), no. 1, 108-119.
  9. K. L. Duggal and B. Sahin, Generalized Cauchy-Riemann lightlike submanifolds of in-definite Sasakian manifolds, Acta Math. Hungar. 112 (2006), no. 1-2, 113-136.
  10. K. L. Duggal and B. Sahin, Lightlike Submanifolds of indefinite Sasakian manifolds, Int. J. Math. Math. Sci. 2007 (2007), Art ID 57585, 1-21.
  11. K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhauser, 2010.
  12. D. H. Jin, Transversal half lightlike submanifolds of an indefinite Sasakian manifold, J. Korean Soc Math. Edu. Ser. B: Pure Appl. Math. 18 (2011), no. 1, 51-61. https://doi.org/10.7468/jksmeb.2011.18.1.051
  13. D. H. Jin, Half lightlike submanifolds of an indefinite Sasakian manifold, J. Korean Soc Math. Edu. Ser. B: Pure Appl. Math. 18 (2011), no. 2, 173-183. https://doi.org/10.7468/jksmeb.2011.18.2.173
  14. D. H. Jin, Special half lightlike submanifolds of an indefinite cosymplectic manifold, J. Funct. Spaces Appl. 2012 (2012), Art ID 636242, 1-16.
  15. D. H. Jin, The curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold, Balkan J. Geom. Appl. 17 (2012), no. 1, 49-57.
  16. D. H. Jin, Non-existence of screen homothetic half lightlike submanifolds of an indefinite Kenmotsu manifold, Balkan J. Geom. Appl. 18 (2013), no. 1, 22-30.
  17. D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite trans-Sasakian manifold, submitted in Balkan J. Geo. Its Appl.
  18. D. H. Jin and J. W. Lee, Generic lightlike submanifolds of an indefinite cosymplectic manifold, Math. Prob. Eng. 2011 (2011), Art ID 610986, 1-16.
  19. T. H. Kang, S. D. Jung, B. H. Kim, H. K. Pak, and J. S. Pak, Lightlike hypersurfaces of indefinite Sasakian manifolds, Indian J. Pure Apple. Math. 34 (2003), no. 9, 1369-1380.
  20. J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187-193.

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