On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold

Yıl 2016, Cilt: 9 Sayı: 1, 45 - 56, 30.04.2016

Süleyman Dirik , Mehmet Atçeken

https://doi.org/10.36890/iejg.591887

Cited By: 2

Öz

In this paper, we study pseudo-slant submanifolds of a Cosymplectic manifold. We research

integrability conditions for the distributions which are involved in the definition of a pseudo-slant

submanifold. The necessary and sufficient conditions are given for a pseudo-slant submanifold to

be pseudo-slant product.

Anahtar Kelimeler

Cosymplectic manifold, Slant submanifold, Pseudo-slant submanifold, Pseudo-slant product

Kaynakça

• [1] Atçeken, M. and Dirik, S., On contact CR-submanifolds of Kenmotsu manifolds, Acta Universitatis Sapientiae, 4(2012), 182-198.
• [2] Atçeken M. and Hui, S. K., Slant and pseudo-slant submanifolds in (LCS)n-manifolds, Czechoslovak Mathematical Journal, 63(2013), 177- 190.
• [3] Atçeken, M. and Dirik, S., On the geometry of pseudo-slant submanifolds of a Kenmotsu manifold, Gulf joural of mathematics, 2(2014), 51-66.
• [4] Blair, D., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematic Springer-Verlog, New York, 509(1976).
• [5] Carriazo, A., New developments in slant submanifolds theory, Narasa Publishing Hause, New Delhi. india, 2000.
• [6] Cabrerizo, J. L. Carriazo, A. Fernandez L. M. and Fernandez, M., Slant submanifolds in Sasakian manifolds, Glasgow Mathematical Journal, 42(2000), 125-138.
• [7] Cabrerizo, J. L. Carriazo, A. Fernandez, L. M. and Fernandez, M., Slant submanifolds in Sasakian manifolds, Geomeatriae Dedicata, 78(1999), 183-199.
• [8] Chand De. U. and. Sarkar, A., On pseudo-slant submanifolds of trans-Sasakian manifolds, Proceedings of the Estonian Academy of Sciences, 60(2011), no.1, 1-11.
• [9] Chen, B.-Y., Geometry of slant submanifolds, Katholieke Universiteit Leuven, Leuven, Belgium, View at Zentralblatt Math., 1990.
• [10] Chen, B.-Y., Slant immersions, Bulletin of the Australian Mathematical Society, 41(1990), 135-147.
• [11] Dirik, S. and Atçeken, M., Pseudo-slant submanifolds of a nearly Cosymplectic manifold, Turkish Journal of Mathematics Computer Science, Article ID 20140035,14 page (2014).
• [12] Khan, V. A and. Khan, M. A., Pseudo-slant submanifolds of a Sasakian manifold, Indian Journal of Pure and Applied Mathematics, 38(2007), 31-42.
• [13] Khan, M. A. Uddin, S. and Singh, K., classification on totally umbilical proper slant and hemi-slant submanifolds of a nearly trans- Sasakian manifold, Differential Differential Geometry - Dynamical Systems, 13(2011), 117-127.
• [14] Khan, M. A., Totally umbilical hemi slant submanifolds of Cosymplectic manifolds, Mathematica Aeterna, 3(2013), no. 8, 845-853.
• [15] Lotta, A., Slant submanifolds in contact geometry, Bulletin Mathematical Society Roumanie, 39(1996), 183-198.
• [16] Papaghuic, N., Semi-slant submanifolds of a Kaehlarian manifold, An. St. Univ. Al. I. Cuza. Univ. Iasi, 40(2009), 55-61.
• [17] 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 physical Scienses, 7(2012), 5538-5544.
• [18] Uddin, S. Bernardine, W. R. 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).