Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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GENERIC SUBMANIFOLDS OF TRANS-SASAKIAN MANIFOLDS WITH CERTAIN VECTOR FIELDS

  • Sarkar, Avijit (Department of Mathematics, University of Kalyani) ;
  • Ghosh, Sujoy (Department of Mathematics, University of Kalyani)
  • Received : 2021.03.11
  • Accepted : 2021.06.11
  • Published : 2021.06.30
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Abstract

The object of the present paper is to deduce some important results on generic submanifolds and generic product of trans-Sasakian manifolds with concurrent vector fields.

Keywords

Acknowledgement

The authors are thankful to the referee for his/her valuable suggestions towards the improvement of the paper.

References

  1. P. Alegre, Semi-invariant submanifolds of Lorentzian Sasakian manifolds, Demonstratio Mathematica, 44 (2011), 391-406. https://doi.org/10.1515/dema-2013-0307
  2. A. Bejancu, CR submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. 69 (1978), 135-142. https://doi.org/10.1090/S0002-9939-1978-0467630-0
  3. A. Bejancu, N. Papaghiuc, Semi-invariant submanifolds of a Sasakian manifold, An. Sti. Univ. "AI. I. Cuza" Iasi Sect. I Mat. 27 (1981), 163-170.
  4. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, Boston-Basel-Berlin, 2002.
  5. B. Y. Chen and S. W. Wei, Riemannian submanifolds with concircular canonical field, Bull. Korean Math. Soc. 56 (2019), 1525-1537. https://doi.org/10.4134/bkms.b181232
  6. B. Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973.
  7. B. Y. Chen, Some results on concircular vector fields and their applications to Ricci solitons, Bull. Korean Math. Soc. 52 (2015), 1535-1547. https://doi.org/10.4134/BKMS.2015.52.5.1535
  8. D. Chinea and P. S. Prestelo, Inavriant submanifolds of a trans-Sasakian manifolds, Publ. Math. Debrecen, 38 (1991), 103-109.
  9. A. De, Totally geodesic submanifolds of trans-Sasakian manifolds, Proc. Estonian Acad. Sci. 62 (2013), 249-257. https://doi.org/10.3176/proc.2013.4.05
  10. U. C. De and A. Sarkar, On three-dimensional trans-Sasakian manifolds, Extracta mathematicae, 23 (2008), 265-277.
  11. U. C. De and A. Sarkar, On pseudo-slant submanifolds of trans-Sasakian manifolds, Proc. Estonian Acad. Sci. 60 (2011), 1-11. https://doi.org/10.3176/proc.2011.1.01
  12. U. C. De and P. Majhi, On invariant submanifolds of Kenmotsu manifolds, J. Geom. 106 (2015), 109-122. https://doi.org/10.1007/s00022-014-0238-y
  13. Th. Friedrich and S. Ivanov, Almost contact manifolds with torsion and parallel spinors, J. Reine Angew. Math. 559 (2003), 217-236.
  14. Z. Guojing, and W. Jianguo, Invariant submanifolds and modes of non-linear autonomous systems, Appl. Math. Mech. 19 (1998), 687-693. https://doi.org/10.1007/BF02452377
  15. M. Kobayashi, Semi-invariant submanifolds of a certain class of almost contact metric manifolds, Tensor (N.S.), 43 (1986), 28-36.
  16. D. L. K. Kumar, H. G. Nagaraja and D. Kumari, Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka-webster connection, J. Math. Comput. Sci. 94 (2019), 447-462.
  17. P. Majhi and G. Ghosh, Concircular vectors field in (κ, µ)-contact metric manifolds, International Electronic Journal of Geometry, 11 (2018), 52-56.
  18. J. C. Marrero, The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl. 162 (1992), 77-86. https://doi.org/10.1007/BF01760000
  19. B. O'Neill, Semi-Riemannian Geometry with Application to Relativity, Pure and Applied Mathematics, 103 (1983).
  20. J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen, 32 (1985), 187-193.
  21. A. Sarkar and 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
  22. S. Sevin,c, G. A. S,ekerci and A. C. Coken, Some results about concircular and concurrent vector fields on pseudo-kaehler manifolds, Journal of Physics, Conferrence series, 766 (2016), 1-6.
  23. S. Sular, and C. Ozgur, On some submanifolds of Kenmotsu manifolds, Chaos, Solitons and Fractals, 42 (2009), 1990-1995. https://doi.org/10.1016/j.chaos.2009.03.185
  24. A. T. Vanli and R. Sari, Invariants submanifolds of trans-Sasakian manifolds, DGDS, 12 (2010), 277-288.
  25. K. Yano and B. Y. Chen, On the Concurrent vector fields of immersed manifolds, Kodai Math. Sem. Rep. 23 (1971), 343-350. https://doi.org/10.2996/kmj/1138846372
  26. K. Yano and M. Kon, Generic submanifolds of sasakian manifolds, Kodai Math. J. 3 (1980), 163-196. https://doi.org/10.2996/kmj/1138036191
  27. H. I. Yoldas, S. E. Meric and E. Yaser, On generic submanifolds of sasakian manifold with concurrent vector field, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2019), 1983-1994.