Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold

Year 2014, Volume 2, 2014, 1 - 14, 26.05.2016

Süleyman Dirik , Mehmet Atçeken

Abstract

In this paper, the geometry of pseudo-slant submanifolds of a nearly Cosymplectic manifold is studied. We obtain the necessary and sufficient conditions on a totally umbilical proper-slant submanifold and show that it is totally geodesic if the mean curvature vector H ∈ µ. well as, we research the integrability conditions of the distributions of pseudo-slant submanifolds and prove some characterizations

Keywords

: Nearly Cosymplectic manifold, Slant submanifold, Proper-slant submanifold, Pseudo-slant submanifold

References

• Atc¸eken, M and Hui, S. K., Slant and Pseudo-Slant Submanifolds in (LCS )n-manifolds, Czechoslovak M. J, 63(138), 177-190 (2013).
• Atc¸eken, M and S. Dirik, Pseudo-slant submanifolds of nearly Kenmotsu manifold, Tsukuba Journal of Mathematics (2014).
• Atc¸eken M and S. Dirik, On contact CR-submanifolds of Kenmotsu manifolds, Acta Univ. sapientiae, mathematica vol. 4, pp. 182-198 (2012).
• Atc¸eken M, Contact CR-submanifolds of Kenmotsu manifolds, Serdica Mathematical. Journal. Vol.37, pp. 67-78(2011).
• Blair, D., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematic Springer-Verlog, New York, Vol. 509 (1976).
• Cabrerizo, J. L., Carriazo, A., Fernandez, L. M., and Fernandez, M., Slant Submanifolds in Sasakian manifolds, Glasgow Math, J. 42:125-138 (2000).
• Carriazo, A., New developments in slant submanifolds theory, Narasa Publishing Hause New Delhi. india (2002).
• Chen, B.Y, Slant immersions, Bull. Austral. Math. Soc. 41:135-147 (1990).
• Khan, V. A, Khan, M. A., and Uddin, S, Totally umbilical semi-invariant submanifolds of a nearly Kenmotsu manifolds, Soochow Journal of Mathematics Vol.33, No. 4, pp. 563-568 (2007).
• Khan, M. A, Uddin, S., and Singh, K., A classification on totally umbilical proper slant and hemi-slant submanifolds of a nearly trans-Sasakian manifold, Differential Geometry - Dynamical Systems, Vol.13, pp. 117-127 (2011).
• Khan, V. A., and Khan M.A, Pseudu-slant submanifolds of a sasakian manifold. India J. Pure Appl., 38,31-42 (2007).
• Kim, J. S., and Liu, X., and Tripathi, M. M., On semi-invariant submanifolds of nearly trans-Sasakian manifolds, Int. J. Pure and Appl. Math. Sci. vol.1 pp.15-34(2004)..
• Lotta, A., Slant Submanifolds in Contact Geometry , Bull. Math. Soc. Romania 39:183-198 (1996).
• Papaghuic, N., Semi-slant submanifolds of a Kaehlarian manifold, An. St. Univ. Al. I. Cuza. Univ. Iasi. 40,55-61(2009).
• S¸ ahin, B., Warped product submanifolds of Kaehler manifolds with a slant factor, Ann. Pol. Math. 95, 2007-226 (2009).
• Turgut Vanli., A. and Sari, R., On invariant submanifolds of nearly Kenmotsu manifolds, Arab. J. Sci. Eng.36, 423-429, (2011).
• Uddin, S¸., Ozel, C., Khan, M. A., and Singh, K., Some classification result on totally umbilical proper slant and hemi slant submanifolds of a nearly Kenmotsu manifold, international journal of pysical Scienses Vol. 7(40), pp 5538-5544 (2012).
• Uddin,S¸., Bernardine R, Wong., and Mustafa, A. A., Warped Product Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold, Hindawi Publishing Corporation Abstract and Applied Analysis, Volume , Article ID 420890, 13 pp, doi:10.1155/2012/420890 (2012).