Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

SLANT LIGHTLIKE SUBMANIFOLDS OF INDEFINITE NEARLY KAEHLER MANIFOLDS

  • Kumar, Tejinder (Department of Mathematics, Maharaja Agrasen University) ;
  • Kumar, Sangeet (Department of Mathematics, Sri Guru Teg Bahadur Khalsa College) ;
  • Kumar, Pankaj (Department of Mathematics, Maharaja Agrasen University)
  • Received : 2021.01.07
  • Accepted : 2021.04.28
  • Published : 2021.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

In the present paper, we introduce the study of slant lightlike submanifolds of indefinite nearly Kaehler manifolds. After proving some geometric results for the existence of slant lightlike submanifolds of indefinite nearly Kaehler manifolds, we give a non-trivial example of this class of lightlike submanifolds. Then, we derive some conditions for the integrability of the distributions associated with slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Consequently, we study totally umbilical slant lightlike submanifolds of indefinite nearly Kaehler manifolds. Subsequently, we investigate minimal slant lightlike submanifolds of indefinite nearly Kaehler manifolds.

Keywords

References

  1. A. Carriazo, Bi-slant immersions, Proc. ICRAMS, Kharagpur, India (2000), 88-97.
  2. A. Gray, Nearly Kaehler manifolds, J. Differ. Geom. 4 (1970), 283-309. https://doi.org/10.4310/jdg/1214429504
  3. A. Lotta, Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie 39 (1996), 183-198.
  4. A. Lotta, Three dimensional slant submanifolds of K-contact manifolds, Balkan J. Geom. Appl. 3 (1998), 37-51.
  5. B. Sahin, Slant lightlike submanifolds of indefinite Hermitian manifolds, Balkan J. Geom. Appl. 13 (2008), 107-119.
  6. B. Sahin, Screen slant lightlike submanifolds, Int. Electron. J. Geom. 2 (2009), 41-54.
  7. B. Sahin, Warped product submanifolds of a Kaehler manifold with a slant factor, Ann. Pol. Math. 95 (2009), 207-226. https://doi.org/10.4064/ap95-3-2
  8. B. Sahin, Slant lightlike submanifolds of indefinite Sasakian manifolds, Filomat 26(2) (2012), 277-287. https://doi.org/10.2298/FIL1202277S
  9. B. Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41 (1990), 135-147. https://doi.org/10.1017/S0004972700017925
  10. B. Y. Chen, Geometry of Slant Submanifolds, Katholieke University, Leuven, 1990.
  11. C. L. Bejan and K. L. Duggal, Global lightlike manifolds and harmonicity, Kodai Math. J. 28 (2005), 131-145. https://doi.org/10.2996/kmj/1111588042
  12. F. Urbano, CR-Submanifolds of Nearly-Kaehler Manifolds, Doctoral thesis, Granada, 1980.
  13. G. Gupta, R. Sachdeva, R. Kumar and R. K. Nagaich, Pointwise slant lightlike sub-manifolds of indefinite Kaehler manifolds, Mediterr. J. Math. 15(3) (2018), Article ID 105.
  14. J. L. Cabrerizo, A. Carriazo, L. M. Fernaandez and M. Fernaandez, Slant submanifolds in Sasakian manifolds, Glasgow Math. J. 42 (2000), 125-138. https://doi.org/10.1017/s0017089500010156
  15. K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Vol. 364 of Mathematics and its Applications, Kluwer Academic Publishers, 1996.
  16. K. L. Duggal and D. H. Jin, Totally umbilical lightlike submanifolds, Kodai Math. J. 26(1) (2003), 49-68. https://doi.org/10.2996/kmj/1050496648
  17. N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Stiins. Univ. Al. I. Cuza Iasi. Math. 9 (1994), 55-61.
  18. R. S. Gupta, A. Upadhyay and A. Sharfuddin, Slant lightlike submanifolds of indefinite Cosymplectic manifolds, Mediterr. J. Math. 8 (2011), 215-227. https://doi.org/10.1007/s00009-010-0077-5
  19. S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge University Press, 1973.
  20. S. S. Shukla and A. Yadav, Semi-slant lightlike submanifolds of indefinite Kaehler manifolds, Revista De La 56(2) (2015), 21-37.