Warped product pseudo-slant submanifolds of (LCS)_n-manifolds

Abstract

The object of the present paper is to study warped product pseudo-slant submanifolds of (LCS)_n-manifolds. We study the existence or non-existence of such submanifolds. The existence is also ensured by an example.

Keywords

• Warped product,pseudo-slant submanifold

References

1. Atceken, M., Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Austral Math. Soc., 77(2) (2008), 177–186.
2. Atceken, M., Warped product semi-slant submanifolds in Kenmotsu manifolds, Turk. J. Math., 34 (2010), 425–432.
3. Atceken, M. and Hui, S. K., Slant and pseudo-slant submanifolds in LCS-manifolds, Czechoslovak Math. J., 63 (2013), 177–190.
4. Bishop, R. L. and O’Neill, B., Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1–49.
5. Cabrerizo, J. L., Carriazo, A., Fernandez, L. M. and Fernandez, M., Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata, 78 (1999), 183-199.
6. Cabrerizo, J. L., Carriazo, A., Fernandez, L. M. and Fernandez, M., Structure on a slant submanifold of a contact manifold, Indian J. Pure Appl. Math., 31 (2000), 857–864.
7. Carriazo, A., New Devolopments in Slant Submanifolds Theory, Narosa Publishing House, New Delhi, India, 2002.
8. Chen, B. Y., Geometry of slant submanifolds, Katholieke Universietit Leuven, 1990.

9. Hui, S. K., On ϕ-pseudosymmetries of (LCS)_n-manifolds, Kyungpook Math. J., 53 (2013), 285–294.
10. Hui, S. K. and Atceken, M., Contact warped product semi-slant submanifolds of (LCS)_n-manifolds, Acta Univ. Sapientiae, Math., 3 (2011), 212–224.
11. Khan, M. A. and Chahal, K. S., Warped product pseudo-slant submanifold of trans-Sasakian manifolds, Thai J. Math., 8 (2010), 263–273.
12. Khan, V. A and Khan, M. A., Pseudo-Slant Submanifolds of a Sasakian Manifold, Indian J. Pure Appl. Math., 38 (2007), 31–42.
13. Khan, V. A, Khan, M. A. and Uddin, S., Warped product submanifolds of cosymplectic manifolds, Balkan J. Geom. Appl., 13 (2008), 55–65.
14. Lotta, A., Slant submanifolds in contact geometry, Bull. Math. Soc. Sci. Math. R. S. Roumanie, 39 (1996), 183–198.
15. Matsumoto, K., On Lorentzian almost paracontact manifolds, Bull. of Yamagata Univ. Nat. Sci., 12 (1989), 151–156.
16. Mihai, I. and Rosca, R., On Lorentzian para-Sasakian manifolds, Classical Analysis, World Scientific Publ., Singapore, (1992), 155–169.
17. O’Neill, B., Semi Riemannian Geometry with applications to relativity, Academic Press, New York, 1983.
18. Papaghiuc, N., Semi-slant submanifolds of a Kaehlerian manifold, An. Sti. Al. I. Cuza, Iasi, 40 (1994), 55–61.
19. Sahin, B., Non-existence of warped product semi-slant submanifolds of Kaehler manifold, Geom. Dedicata, 117 (2006), 195–202.
20. Shaikh, A. A., On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J., 43 (2003), 305–314.
21. Shaikh, A. A., Some results on (LCS)_n-manifolds, J. Korean Math. Soc., 46 (2009), 449–461.
22. Shaikh, A. A. and Baishya, K. K., On concircular structure spacetimes, J. Math. Stat., 1 (2005), 129–132.
23. Shaikh, A. A. and Baishya, K. K., On concircular structure spacetimes II, American J. Appl. Sci., 3(4) (2006), 1790–1794.
24. Shaikh, A. A., Basu, T. and Eyasmin, S., On locally ϕ-symmetric (LCS)_n-manifolds, Int. J. Pure Appl. Math., 41 (2007), 1161–1170.
25. Shaikh, A. A., Basu, T. and Eyasmin, S., On the existence of ϕ-recurrent (LCS)_n-manifolds, Extracta Mathematicae, 23 (2008), 71–83.
26. Shaikh, A. A. and Binh, T. Q., On weakly symmetric (LCS)_n-manifolds, J. Adv. Math. Studies, 2 (2009), 75–90.
27. Shaikh, A. A. and Hui, S. K., On generalized ϕ-recurrent (LCS)_n-manifolds, AIP Conference Proceedings, 1309 (2010), 419–429.
28. Uddin, S., Warped product CR-submanifolds of LP-cosymplectic manifolds, Filomat, 24 (2010), 87–95.
29. Uddin, S., Khan, V. A. and Khan, K. A., Warped product submanifolds of a Kenmotsu manifold, Turk. J. Math., 36 (2012), 319–330.
30. Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad. Tokyo, 16 (1940), 195–200.