Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

CERTAIN RESULTS ON SUBMANIFOLDS OF GENERALIZED SASAKIAN SPACE-FORMS

  • Yadav, Sunil Kumar (Department of Mathematics, Poornima college of Engineering) ;
  • Chaubey, Sudhakar K (Section of Mathematics, Department of Information Technology, Shinas College of Technology)
  • Received : 2019.04.16
  • Accepted : 2019.08.26
  • Published : 2020.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian space-forms. We deduce some results related to the invariant and anti-invariant slant submanifolds of the generalized Sasakian spaceforms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical submanifolds of the generalized Sasakian space-forms. To prove the existence of almost semiinvariant and anti-invariant submanifolds, we provide the non-trivial examples.

Keywords

References

  1. P. Alegre, D. E. Blair, A. Carriazo, Generalized Sasakian-space-forms, Israel. J. Math. 14 (2004), 157-183.
  2. P. Alegre, A. Carriazo, Structure on Generalized Sasakian-space-forms, Diff. Geo. and its Application 26 (2008), 656-666. https://doi.org/10.1016/j.difgeo.2008.04.014
  3. P. Alegre, A. Carriazo, Submanifolds of Generalized Sasakian-space-forms, Taiwanese J. Maths 13 (2009), 923-941.
  4. P. Alegre, A. Carriazo, Generalized Sasakian-space-forms and conformal change of metric, Results in Maths. 24 (2011), 485-493.
  5. R. Al-Ghefari, F. R. Al-Solamy, M. H. Shahid, CR-submanifolds of generalized Sasakian-space-forms, JPJ. Geom. and Topology 6 (2006), 151-166.
  6. A. Bejancu, CR-submanifolds of Kahler manifold, Proc. Amer. Math. Soc. 69(1) (1978), 134-142.
  7. M. Belkhelfa, R. Desecz, L. Verstraelen, Symmetry properties of generalized Sasakian-space-forms, Soochow J. Maths. 3 (2005), 611-616.
  8. A. Bejancu, N. Papaghuec, Semi-invariant submanifolds of Sasakian manifolds, An sti. uni.'ALI CUZA'Iadi. 27 (1981), 161-170.
  9. A. Bejancu, CR-submanifolds of Kahler manifold, Proc. Amer. Math. Soc. 69(1) (1978), 134-142.
  10. M. Barros, F. Urbano, CR-Submanifolds of generalized Complex space-forms, Diff. Geom. 26 (2008), 656-666. https://doi.org/10.1016/j.difgeo.2008.04.014
  11. D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer-Verlag, 1976.
  12. A. Bejancu, N. Papaghuec, Almost Semi-invariant submanifolds of Sasakian manifolds, Bull. Math. Soc Math. R. S. Roumanie 28 (1984), 13-40.
  13. A. Carriazo, On generalized Sasakian-space-forms, Proceeding of the Ninth International workshop on diff. Geom. 9 (2005), 31-39.
  14. S. K. Chaubey, A. Yildiz, On Ricci tensor in the generalized Sasakian-space-forms, International Journal of Maps in Mathematics 2 (1) (2019), 131-147.
  15. S. K. Chaubey, S. K. Yadav, W-semisymmetric generalized Sasakian-space-forms, Adv. Pure Appl. Math. 2018, https://doi.org/10.1515/apam-2018-0032.
  16. B. Y. Chen, Geometry of slant submanifolds, Katholieke, Universities Lauren, 1990.
  17. J. A. Cabrerizo, A. Carriazo, L. M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasgow Mathematical Journal 42 (2000), 125-138. https://doi.org/10.1017/s0017089500010156
  18. U. C. De, A. Sarkar, Some results on generalized Sasakian-space-forms, Thai journal of Mathematics 8 (2010), 1-10.
  19. F. Gherib, M. Gorine, M. Belkhelfa, Parallel and semi-symmetric of some tensor in generalized Sasakian-space-forms, Bull. Trans. Univ. Brasav, Series Mathematics, informatics, Physics, 1 (50) (2008), 139-148.
  20. Z. Guajing, W. Jiangu, Invariant submanifolds and models if non-linear autonomous system, Appl. Math. and Mech. 19 (1998), 687-693. https://doi.org/10.1007/BF02452377
  21. U. K. Kim, Conformally flat generalized Sasakian-space-forms, Note di Matematica 26 (2006), 55-67.
  22. H. B. Karadog, M. Atceken, Invariant submanifolds of Sasakian manifolds, Balkan J. Geom. Appl. 12 (2007), 68-75.
  23. K. Kenmotsu, Invariant submanifolds of Sasakian manifolds, Tohoku Math. J. 21 (1969), 495-500. https://doi.org/10.2748/tmj/1178242959
  24. M. Kon, Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep. 25 (1973), 330-336. https://doi.org/10.2996/kmj/1138846821
  25. G. S. Ronsse, Generic and skew CR-submanifolds of a Kahler manifold, Bull. Inst. Math. Acsd sci. 18 (1990), 127-141.
  26. A. Sarkar, M. Sen, On invariant submanifolds of trans-Sasakian manifolds, Proc. Estonian Acad. Sci 61 (2012), 29-37. https://doi.org/10.3176/proc.2012.1.04
  27. A. A. Shaikh, Y. Matsuyama, S. K. Hui, On Invariant submanifolds of $(LCS)_n$ manifolds, Journal of the Egyptian Math Sci. 24 (2016), 263-269. https://doi.org/10.1016/j.joems.2015.05.008
  28. M. D. Siddiqi, On almost semi-invariant ${\xi}^{\bot}$-submanifolds of a para Kenmotsu Manifold, South Asian Journal of Mathematics 6(3) (2016), 140-151.
  29. M. D. Siddiqi, A. Haseeb, M. Ahmed, Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds, Carpathian Math. Publ. 9(2) (2017), 188197.
  30. M. M. Tripathi, I. Mihai, On submanifolds of framed metric manifolds, Note Mat. 20(2) (2001), 135-164.
  31. M. M. Tripathi, K. D. Singh, Almost semi-invariant submanifolds of an $\xi$-framed metric manifolds, Demonstratio Math. 29 (1996), 413-426. https://doi.org/10.1515/dema-1996-0218
  32. M. M. Tripathi,Generic submanifolds of generalized complex space-forms, Publ. Math. Debrecen, 50 (1997), 373-392.
  33. K. Yano, S. Ishihara, Invariant submanifolds of almost contact manifolds, Kodai Math. Sem. Rep. 21 (1969), 350-364. https://doi.org/10.2996/kmj/1138845942
  34. A. Yiddiz, C. Murathan, Invariant submanifolds of Sasakian-space-forms, J. Geom. 95 (2009), 135-150. https://doi.org/10.1007/s00022-009-0011-9
  35. S. K. Yadav, D. L. Suthar, Semi-invariant $\xi$-submanifolds of trans-Sasakian manifolds, Caspian Journal of Applied Science Research, 2(2) (2013), 23-28.