Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

INDEFINITE GENERALIZED SASAKIAN SPACE FORM ADMITTING A GENERIC LIGHTLIKE SUBMANIFOLD

  • Jin, Dae Ho (Department of Mathematics Dongguk University)
  • Received : 2013.10.31
  • Published : 2014.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a generic lightlike submanifold M subject such that the structure vector field of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

Keywords

References

  1. 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
  2. C. Calin, Contributions to geometry of CR-submanifold, Thesis, University of Iasi, Romania, 1998.
  3. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  4. 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
  5. K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  6. 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.
  7. K. L. Duggal and B. Sahin, Generalized Cauchy-Riemann lightlike Submanifolds of indefinite Sasakian manifolds, Acta Math. Hungar. 112 (2006), no. 1-2, 107-130. https://doi.org/10.1007/s10474-006-0068-y
  8. K. L. Duggal and B. Sahin, Lightlike Submanifolds of indefinite Sasakian manifolds, Int. J. Math. Math. Sci. 2007 (2007), Art ID 57585, 1-21.
  9. K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser, 2010.
  10. D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold, Indian J. Pure Appl. Math. 41 (2010), no. 4, 569-581. https://doi.org/10.1007/s13226-010-0032-y
  11. 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
  12. D. H. Jin, Half lightlike submanifold of an indefinite Sasakian manifold, J. Korean Soc. Math. Edu. Ser. B Pure Appl. Math. 18 (2011), no. 2, 173-183.
  13. D. H. Jin, The curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold, Balkan J. Geom. Appl. 17 (2012), no. 1, 49-57.
  14. 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.
  15. D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite cosymplectic manifold, Commun. Korean Math. Soc. 27 (2012), no. 1, 185-195. https://doi.org/10.4134/CKMS.2012.27.1.185
  16. D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite trans-Sasakian manifold, submitted in Balkan J. Geom. Appl. https://doi.org/10.1007/s13226-010-0032-y
  17. D. H. Jin and J. W. Lee, Generic lightlike submanifolds of an indefinite cosymplectic manifold, Math. Probl. Eng. 2011 (2011), Art ID 610986, 16 pp.
  18. 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 Appl. Math. 34 (2003), no. 9, 1369-1380.
  19. U. H. Ki and D. H. Jin, Generic submanifolds with parallel Ricci curvature of $S^{2m+1}$(1), J. Korean Math. Soc. 19 (1982), no. 1, 55-60.
  20. U. H. Ki and D. H. Jin, Infinitesimal variations preserving the Ricci tensor of generic submanifolds of an odd-dimensional sphere, Kyungpook Math. J. 22 (1982), no. 2, 317-324.
  21. D. N. Kupeli, Singular Semi-Riemannian Geometry, Mathematics and Its Applications, vol. 366, Kluwer Acad. Publishers, Dordrecht, 1996.
  22. J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187-193.
  23. A. Upadhyay, R. S. Gupta, and A. Sharfuddin, Semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces of an indefinite generalized Sasakian space form, International Electronic Journal of Geometry. 5 (2012), no. 1, 140-150.