대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제29권4호
  • /
  • Pages.539-547
  • /
  • 2014
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE KAEHLER MANIFOLDS ADMITTING NON-METRIC π-CONNECTIONS

  • Jin, Dae Ho (Department of Mathematics Dongguk University)
  • 투고 : 2013.12.16
  • 발행 : 2014.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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

키워드

참고문헌

  1. N. S. Ageshe and M. R. Chafle, A semi-symmetric non-metric 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. A. Barman, On a type of quarter-symmetric non-metric $\phi$-connection on a Kenmotsu manifold, Bull. Math. Analy. Appl. 4 (2012), no. 3, 1-11.
  4. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  5. K. L. Duggal and D. H. Jin, Half-lightlike submanifolds of codimension 2, Math. J. Toyama Univ. 22 (1999), 121-161.
  6. K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
  7. K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, Birkhauser, 2010.
  8. 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
  9. S. Golab, On semi-symmetric and quarter-symmetric connections, Tensor (N.S.) 29 (1975), no. 3, 249-254.
  10. D. H. Jin, Screen conformal lightlike real hypersurfaces of an indefinite complex space form, Bull. Korean Math. Soc. 47 (2010), no. 2, 341-353. https://doi.org/10.4134/BKMS.2010.47.2.341
  11. D. H. Jin, Lightlike real hypersurfaces with totally umbilical screen distributions, Commun. Korean Math. Soc. 25 (2010), no. 3, 443-450. https://doi.org/10.4134/CKMS.2010.25.3.443
  12. D. H. Jin, Geometry of screen conformal real half lightlike submanifolds, Bull. Korean Math. Soc. 47 (2010), no. 4, 701-714. https://doi.org/10.4134/BKMS.2010.47.4.701
  13. D. H. Jin, Real half lightlike submanifolds with totally umbilical properties, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 17 (2010), no. 1, 51-63.
  14. D. H. Jin, Real half lightlike submanifolds of an indefinite Kaehler manifold, Commun. KoreaD. H. Jinn Math. Soc. 26 (2011), no. 4, 635-647. https://doi.org/10.4134/CKMS.2011.26.4.635
  15. D. H. Jin, Lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection, J. Korean Soc Math. Edu. Ser. B Pure Appl. Math. 19 (2012), no. 3, 211-228. https://doi.org/10.7468/jksmeb.2012.19.3.211
  16. 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
  17. D. H. Jin, Einstein half lightlike submanifolds of a Lorentzian space form with a semisymmetric non-metric connection, J. Inequal. Appl. 2013 (2013), 403, 13 pp. https://doi.org/10.1186/1029-242X-2013-13
  18. 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
  19. J. Nikic and N. Pusic, A remakable class of natural metric quarter-symmetric connection on a hyperbolic Kaehler space, Conference "Applied Differential Geometry: General Relativity"-Workshop "Global Analysis, Differential Geometry, Lie Algebras", 96-101, BSG Proc., 11, Geom. Balkan Press, Bucharest, 2004.
  20. N. Pusic, On quarter-symmetric metric connections on a hyperbolic Kaehler space, Publ. de l' Inst. Math. 73(87) (2003), 73-80. https://doi.org/10.2298/PIM0373073P
  21. A. A. Shaikh and S. K. Jana, On quarter symmetric metric connections on a (k,m)- contact metric manifolds, Commun. Fac. Sci. Univ. Ank. Series A1 55 (2006), no. 1, 33-45.
  22. 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.
  23. 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.

피인용 문헌

  1. Radical screen transversal lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection pp.1793-6977, 2017, https://doi.org/10.1142/S021988781850024X