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Indefinite Generalized Sasakian Space Form Admitting a Lightlike Hypersurface

  • JIN, DAE HO (Department of Mathematics, Dongguk University)
  • 투고 : 2013.09.17
  • 심사 : 2015.10.01
  • 발행 : 2015.12.23

초록

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

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참고문헌

  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, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  5. K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhauser, 2010.
  6. D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold, Indian J. of Pure and Applied Math., 41(4)(2010), 569-581. https://doi.org/10.1007/s13226-010-0032-y
  7. D. H. Jin, The curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold, Balkan J. Geo. Its Appl., 17(1)(2012), 49-57.
  8. D. H. Jin, Non-existence of screen homothetic half lightlike submanifolds of an indefinite Kenmotsu manifold, Balkan J. Geo. Its Appl., 18(1)(2013), 22-30.
  9. D. H. Jin, Geometry of lightlike hypersurfaces of an indefinite cosymplectic manifold, Commun. Korean Math. Soc., 27(1)(2012), 185-195. https://doi.org/10.4134/CKMS.2012.27.1.185
  10. D. H. Jin and J. W. Lee, Generic lightlike submanifolds of an indefinite cosymplectic manifold, Math. Prob. in Engineering, 2011, Art ID 610986, 1-16.
  11. 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 and Apple., Math., 34(2003), 1369-1380.
  12. J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen, 32(1985), 187-193.