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NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE TRANS-SASAKIAN MANIFOLDS WITH NON-METRIC πœƒ-CONNECTIONS

  • Jin, Dae Ho (Department of Mathematics Dongguk University)
  • 투고 : 2014.04.30
  • λ°œν–‰ : 2015.01.31
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초둝

We study two types of 1-lightlike submanifolds, so-called lightlike hypersurface and half lightlike submanifold, of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric ${\theta}$-connection. We prove that there exist no such two types of 1-lightlike submanifolds of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric ${\theta}$-connections.

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  1. N. S. Agashe and M. R. Chafle, A semi-symmetric nonmetric connection on a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), no. 6, 399-409.
  2. M. Ahmad and A. Haseeb, Hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter-symmetric non-metric connection, Kyungpook Math. J. 49 (2009), no. 3, 533-543. https://doi.org/10.5666/KMJ.2009.49.3.533
  3. 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
  4. A. Barman, On a type of quarter-symmetric non-metric ${\phi}$-connection on a Kenmotsu manifold, Bull. Math. Anal. Appl. 4 (2012), no. 3, 1-11.
  5. C. Calin, Contributions to geometry of CR-submanifold, Thesis, University of Iasi (Romania), 1998.
  6. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  7. K. L. Duggal and D. H. Jin, Half-lightlike submanifolds of codimension 2, Math. J. Toyama Univ. 22 (1999), 121-161.
  8. K. L. Duggal and D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  9. K. L. Duggal and D. H. Jin, Generic lightlike submanifolds of an indefinite Sasakian manifold, Int. Electron. J. Geom. 5 (2010), no. 1, 108-119.
  10. K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser, 2010.
  11. A. Friedmann and J. A. Schouten, Uber die Geometric der halbsymmetrischen Ubertragung, Math. Z. 21 (1924), no. 1, 211-223. https://doi.org/10.1007/BF01187468
  12. S. Golab, On semi-symmetric and quarter-symmetric connections, Tensor (N.S.) 29 (1975), no. 3, 249-254.
  13. 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
  14. D. H. Jin, Transversal half lightlike submanifolds of an indefinite Sasakian manifold, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 18 (2011), no. 1, 51-61. https://doi.org/10.7468/jksmeb.2011.18.1.051
  15. D. H. Jin, Half lightlike submanifolds of an indefinite Sasakian manifold, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 18 (2011), no. 2, 173-183. https://doi.org/10.7468/jksmeb.2011.18.2.173
  16. D. H. Jin, The curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold, Balkan J. Geom. Appl. 17 (2012), no. 1, 49-57.
  17. 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
  18. D. H. Jin, Lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 19 (2012), no. 3, 211-228. https://doi.org/10.7468/jksmeb.2012.19.3.211
  19. 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.
  20. D. H. Jin, Einstein lightlike hypersurfaces of a Lorentz space form with a semi-symmetric non-metric connection, Bull. Korean Math. Soc. 50 (2013), no. 4, 1367-1376. https://doi.org/10.4134/BKMS.2013.50.4.1367
  21. D. H. Jin, Einstein half lightlike submanifolds of a Lorentzian space form with a semisymmetric non-metric connection, J. Ineqal. Appl. 2013 (2013), 403, 13 pp. https://doi.org/10.1186/1029-242X-2013-403
  22. D. H. Jin and J. W. Lee, Generic lightlike submanifolds of an indefinite cosymplectic manifold, Math. Prob. Eng. 2011 (2011), Art ID 610986, 16 pp.
  23. D. H. Jin and J. W. Lee, A classification of half lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection, Bull. Korean Math. Soc. 50 (2013), no. 3, 705-717. https://doi.org/10.4134/BKMS.2013.50.3.705
  24. J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187-193.
  25. S. Sasaki, Almost contact manifolds, Lecture notes, Math. Inst., Tohoku Univ., Vol. I, II, III, 1965-1968.
  26. S. Yadav and D. L. Suthar, A quart symmetric non-metric connection in a generalized co-symmpletic manifolds, Glob. J. Sci. Fron. Res. 11 (2011), no. 9, 1-7.
  27. E. Yasar, A. C. Coken, and A. Yucesan, Lightlike hypersurfaces in semi-Riemannian manifold with semi-symmetric non-metric connection, Math. Scand. 102 (2008), no. 2, 253-264. https://doi.org/10.7146/math.scand.a-15061