Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD WITH AN (ℓ, m)-TYPE METRIC CONNECTION

  • Jin, Dae Ho (Department of Mathematics Education Dongguk University)
  • Received : 2018.03.27
  • Accepted : 2018.07.30
  • Published : 2019.04.30
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Abstract

We study generic lightlike submanifolds M of an indefinite trans-Sasakian manifold ${\bar{M}}$ or an indefinite generalized Sasakian space form ${\bar{M}}(f_1,f_2,f_3)$ endowed with an $({\ell},m)$-type metric connection subject such that the structure vector field ${\zeta}$ of ${\bar{M}}$ is tangent to M.

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References

  1. P. Alegre, D. E. Blair, and A. Carriazo, Generalized Sasakian-space-forms, 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. G. de Rham, Sur la reductibilite d'un espace de Riemann, Comment. Math. Helv. 26 (1952), 328-344. https://doi.org/10.1007/BF02564308
  4. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Mathematics and its Applications, 364, Kluwer Academic Publishers Group, Dordrecht, 1996.
  5. K. L. Duggal and D. J. Jin, Generic lightlike submanifolds of an indefinite Sasakian manifold, Int. Electron. J. Geom. 5 (2012), no. 1, 108-119.
  6. H. A. Hayden, Sub-spaces of a space with torsion, Proc. London Math. Soc. (2) 34 (1932), no. 1, 27-50. https://doi.org/10.1112/plms/s2-34.1.27
  7. D. H. Jin, Indefinite generalized Sasakian space form admitting a generic lightlike submanifold, Bull. Korean Math. Soc. 51 (2014), no. 6, 1711-1726. https://doi.org/10.4134/BKMS.2014.51.6.1711
  8. D. H. Jin, Generic lightlike submanifolds of an indefinite trans-Sasakian manifold of a quasi-constant curvature, Appl. Math. Sci. 9 (2015), no. 60, 2985-2997.
  9. D. H. Jin, Lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an ($\ell$, m)-type metric connection, Far East J. Math. Sci. 103 (2018), no. 8, 1323-1343. https://doi.org/10.17654/ms103081323
  10. D. H. Jin and J. W. Lee, Generic lightlike submanifolds of an indefinite cosymplectic manifold, Math. Probl. Eng. 2011 (20111), Art. ID 610986, 16 pp.
  11. D. H. Jin and J. W. Lee, Half lightlike submanifolds of a semi-Riemannian manifold of quasi-constant curvature, Filomat 30 (2016), no. 7, 1737-1745. https://doi.org/10.2298/FIL1607737J
  12. D. H. Jin and J. W. Lee, Generic lightlike submanifolds of an indefinite Kaehler manifold, Inter. J. Pure Appl. Math. 101 (2015), no. 4, 543-560.
  13. D. N. Kupeli, Singular Semi-Riemannian Geometry, Mathematics and its Applications, 366, Kluwer Academic Publishers Group, Dordrecht, 1996.
  14. J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187-193.
  15. K. Yano, On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl. 15 (1970), 1579-1586.
  16. K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.) 38 (1982), 13-18.