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

Year 2016, Volume: 9 Issue: 1, 45 - 56, 30.04.2016

Süleyman Dirik Mehmet Atçeken

https://doi.org/10.36890/iejg.591887
Cited By: 2

Abstract

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.

Keywords

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

References

  • [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).

Year 2016, Volume: 9 Issue: 1, 45 - 56, 30.04.2016

Süleyman Dirik Mehmet Atçeken

https://doi.org/10.36890/iejg.591887
Cited By: 2

Abstract

References

  • [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).
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Süleyman Dirik

Mehmet Atçeken This is me

Publication Date April 30, 2016
Published in Issue Year 2016 Volume: 9 Issue: 1

Cite

APA Dirik, S., & Atçeken, M. (2016). On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold. International Electronic Journal of Geometry, 9(1), 45-56. https://doi.org/10.36890/iejg.591887
AMA Dirik S, Atçeken M. On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold. Int. Electron. J. Geom. April 2016;9(1):45-56. doi:10.36890/iejg.591887
Chicago Dirik, Süleyman, and Mehmet Atçeken. “On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold”. International Electronic Journal of Geometry 9, no. 1 (April 2016): 45-56. https://doi.org/10.36890/iejg.591887.
EndNote Dirik S, Atçeken M (April 1, 2016) On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold. International Electronic Journal of Geometry 9 1 45–56.
IEEE S. Dirik and M. Atçeken, “On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold”, Int. Electron. J. Geom., vol. 9, no. 1, pp. 45–56, 2016, doi: 10.36890/iejg.591887.
ISNAD Dirik, Süleyman - Atçeken, Mehmet. “On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold”. International Electronic Journal of Geometry 9/1 (April 2016), 45-56. https://doi.org/10.36890/iejg.591887.
JAMA Dirik S, Atçeken M. On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold. Int. Electron. J. Geom. 2016;9:45–56.
MLA Dirik, Süleyman and Mehmet Atçeken. “On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold”. International Electronic Journal of Geometry, vol. 9, no. 1, 2016, pp. 45-56, doi:10.36890/iejg.591887.
Vancouver Dirik S, Atçeken M. On the Geometry of Pseudo-Slant Submanifolds of a Cosymplectic Manifold. Int. Electron. J. Geom. 2016;9(1):45-56.

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