Korean J. Math. Vol. 29 No. 2 (2021) pp.425-434
DOI: https://doi.org/10.11568/kjm.2021.29.2.425

Generic submanifolds of trans-Sasakian manifolds with certain vector fields

Main Article Content

Avijit Sarkar
Sujoy Ghosh

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.


Article Details

References

[1] P. Alegre, Semi-invariant submanifolds of Lorentzian Sasakian manifolds, Demonstratio Mathematica, 44 (2011), 391–406. Google Scholar

[2] A. Bejancu, CR submanifolds of a Kaehler manifold I, Proc. Amer. Math. Soc. 69 (1978), 135–142. Google Scholar

[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. Google Scholar

[4] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkha ̈user, Boston– Basel–Berlin, 2002. Google Scholar

[5] B. Y. Chen and S. W. Wei, Riemannian submanifolds with concircular canonical field, Bull. Korean Math. Soc. 56 (2019), 1525–1537. Google Scholar

[6] B. Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973. Google Scholar

[7] B. Y. Chen, Some results on concircular vector fields and their applications to Ricci solitons, Bull. Korean Math. Soc. 52 (2015), 1535–1547. Google Scholar

[8] D. Chinea and P. S. Prestelo, Inavriant submanifolds of a trans-Sasakian manifolds, Publ. Math. Debrecen, 38 (1991), 103–109. Google Scholar

[9] A. De, Totally geodesic submanifolds of trans-Sasakian manifolds, Proc. Estonian Acad. Sci. 62 (2013), 249–257. Google Scholar

[10] U. C. De and A. Sarkar, On three-dimensional trans-Sasakian manifolds, Extracta mathematicae, 23 (2008), 265–277. Google Scholar

[11] U. C. De and A. Sarkar, On pseudo-slant submanifolds of trans-Sasakian manifolds, Proc. Es- tonian Acad. Sci. 60 (2011), 1–11. Google Scholar

[12] U. C. De and P. Majhi, On invariant submanifolds of Kenmotsu manifolds, J. Geom. 106 (2015), 109–122. Google Scholar

[13] Th. Friedrich and S. Ivanov, Almost contact manifolds with torsion and parallel spinors, J. Reine Angew. Math. 559 (2003), 217–236. Google Scholar

[14] Z. Guojing, and W. Jianguo, Invariant submanifolds and modes of non-linear autonomous sys- tems, Appl. Math. Mech. 19 (1998), 687–693. Google Scholar

[15] M. Kobayashi, Semi-invariant submanifolds of a certain class of almost contact metric mani- folds, Tensor (N.S.), 43 (1986), 28–36. Google Scholar

[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. Google Scholar

[17] P. Majhi and G. Ghosh, Concircular vectors field in (κ,μ)-contact metric manifolds, International Electronic Journal of Geometry, 11 (2018), 52–56. Google Scholar

[18] J. C. Marrero, The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl. 162 (1992), 77–86. Google Scholar

[19] B. O’Neill, Semi-Riemannian Geometry with Application to Relativity, Pure and Applied Mathematics, 103 (1983). Google Scholar

[20] J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen, 32 (1985), 187-193. Google Scholar

[21] A. Sarkar and M. Sen, On invariant submanifolds of trans-sasakian manifolds, Proc. Estonian Acad. Sci. 61 (2012), 29–37. Google Scholar

[22] S. Sevin ̧c, G. A. S ̧ekerci and A. C. C ̧ ̈oken, Some results about concircular and concurrent vector fields on pseudo-kaehler manifolds, Journal of Physics, Conferrence series, 766 (2016), 1–6. Google Scholar

[23] S. Sular, and C. O ̈zgu ̈r, On some submanifolds of Kenmotsu manifolds, Chaos, Solitons and Fractals, 42 (2009), 1990–1995. Google Scholar

[24] A. T. Vanli and R. Sari, Invariants submanifolds of trans-Sasakian manifolds, DGDS, 12 (2010), 277–288. Google Scholar

[25] K. Yano and B. Y. Chen, On the Concurrent vector fields of immersed manifolds, Kodai Math. Sem. Rep. 23 (1971), 343–350. Google Scholar

[26] K. Yano and M. Kon, Generic submanifolds of sasakian manifolds, Kodai Math. J. 3 (1980), 163–196. Google Scholar

[27] H. I. Yolda ̧s, S ̧. E. Meri ̧c and E. Ya ̧ser, On generic submanifolds of sasakian manifold with concurrent vector field, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2019), 1983– 1994. Google Scholar