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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).

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

Süleyman Dirik Mehmet Atçeken

Abstract

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).
There are 18 citations in total.

Details

Other ID JA22TG64YB
Journal Section Articles
Authors

Süleyman Dirik

Mehmet Atçeken

Publication Date May 26, 2016
Published in Issue Year 2014 Volume 2, 2014

Cite

APA Dirik, S., & Atçeken, M. (2016). Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold. Turkish Journal of Mathematics and Computer Science, 2(1), 1-14.
AMA Dirik S, Atçeken M. Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold. TJMCS. May 2016;2(1):1-14.
Chicago Dirik, Süleyman, and Mehmet Atçeken. “Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold”. Turkish Journal of Mathematics and Computer Science 2, no. 1 (May 2016): 1-14.
EndNote Dirik S, Atçeken M (May 1, 2016) Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold. Turkish Journal of Mathematics and Computer Science 2 1 1–14.
IEEE S. Dirik and M. Atçeken, “Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold”, TJMCS, vol. 2, no. 1, pp. 1–14, 2016.
ISNAD Dirik, Süleyman - Atçeken, Mehmet. “Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold”. Turkish Journal of Mathematics and Computer Science 2/1 (May 2016), 1-14.
JAMA Dirik S, Atçeken M. Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold. TJMCS. 2016;2:1–14.
MLA Dirik, Süleyman and Mehmet Atçeken. “Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold”. Turkish Journal of Mathematics and Computer Science, vol. 2, no. 1, 2016, pp. 1-14.
Vancouver Dirik S, Atçeken M. Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold. TJMCS. 2016;2(1):1-14.