Some Properties of *CR*-Submanifolds of a Nearly Trans-Sasakian Manifold with a Semi Symmetric Non-Metric Connection

Affiliation(s)

Department of Mathematics, Kent State University, Kent, USA.

Department of Mathematics, Integral University, Lucknow, India.

Department of Mathematics, Kent State University, Kent, USA.

Department of Mathematics, Integral University, Lucknow, India.

ABSTRACT

This paper deals with the study of *CR*-submanifolds of a nearly
trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis
tensor, integrability conditions for some distributions on *CR*-submanifolds of a nearly
trans-Sasakian manifold with a semi symmetric non- metric connection are
discussed.

KEYWORDS

*CR* -Submanifolds,
Nearly Trans-Sasakian Manifold,
Semi Symmetric Non-Metric Connection,
Distribution

Cite this paper

Das, L. , Ahmad, M. and Haseeb, A. (2014) Some Properties of*CR*-Submanifolds of a Nearly Trans-Sasakian Manifold with a Semi Symmetric Non-Metric Connection. *Journal of Applied Mathematics and Physics*, **2**, 813-822. doi: 10.4236/jamp.2014.28090.

Das, L. , Ahmad, M. and Haseeb, A. (2014) Some Properties of

References

[1] Bejancu, A. (1978) -Submanifolds of a Kaehler Manifold I. Proceedings of the American Mathematical Society, 69, 135-142.

[2] Kobayashi, M. (1981) -Submanifolds of Sasakian Manifold. Tensor, N. S., 35, 297-307.

[3] Yano, K. and Kon, M. (1989) On Contact -Submanifolds. Journal of the Korean Mathematical Society, 26, 231-262.

[4] Oubina, J.A. (1985) New Class of Almost Contact Metric Structures. Publicationes Mathematicae Debrecen, 32, 187-193.

[5] Janssens, D. and Vanhecke, L. (1981) Almost Contact Structures and Curvature Tensors. Kodai Mathematical Journal, 1, 1-27. http://dx.doi.org/10.2996/kmj/1138036310

[6] Bejancu, A. and Papaghuic, N. (1984) -Submanifolds of a Kenmotsu Manifold. Rendiconti di Matematica, 7, 607-622.

[7] Shahid, M.H. (1991) -Submanifolds of a Trans-Sasakian Manifold. Indian Journal of Pure and Applied Mathematics, 22, 1007-1012.

[8] Shahid, M.H. (1994) -Submanifolds of a Trans-Sasakian Manifold II. Indian Journal of Pure and Applied Mathematics, 25, 299-307.

[9] Al-Solamy, F.R. (2002) -Submanifolds of a Nearly Trans-Sasakian Manifold. IJMMS, 31, 167-175.

[10] Ahmad, M., Ozgür, C. and Haseeb, A. -Submanifolds of an -Sasakian Manifold with a Semi-Symmetric Metric Connection. Hacettepe Journal of Mathematics and Statistics.?

[11] Das, L.S. and Ahmad, M. (2009) -Submanifolds of an -Sasakian Manifold with a Quarter Symmetric NonMetric Connection. Mathematical Sciences Research Journal, 13, 161-169.

[12] Das, L.S., Ahmad, M. and Haseeb, A. (2011) Semi-Invariant Submanifolds of a Nearly Sasakian Manifold Endowed with a Semi-Symmetric Non-Metric Connection. Journal of Applied Analysis, 17, 1-12.

[13] Tripathi, M.M. (2004) On Semi-Invariant Submanifolds of Nearly Trans-Sasakian Manifolds. The International Journal of Pure and Applied Mathematical Sciences, 1, 15-34.

[14] Golab, S. (1975) On Semi-Symmetric and Quarter Symmetric Linear Connections. Tensor, N. S., 29, 249-254.

[15] Blair, D.E. (1976) Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics. Vol. 509, SpringerVerlag, Berlin.

[16] Gray, A. and Hervella, L.M. (1980) The Sixteen Classes of Almost Hermitian Manifolds and Their Linear Invariants. Annali di Matematica Pura ed Applicata, 4, 35-58. http://dx.doi.org/10.1007/BF01796539

[17] Blair, D.E. and Oubina, J.A. (1990) Conformal and Related Changes of Metric on the Product of Two Almost Contact Metric Manifolds. Publications Mathematiques, 34, 199-207.

http://dx.doi.org/10.5565/PUBLMAT_34190_15

[18] Gherghe, C. (2000) Harmonicity on Nearly Trans-Sasaki Manifolds. Demonstratio Mathematica, 33, 151-157.

[19] Blair, D.E., Showers, D.K. and Yano, K. (1996) Nearly Sasakian Structures. Kodai Mathematical Journal, 27, 175-180.

[1] Bejancu, A. (1978) -Submanifolds of a Kaehler Manifold I. Proceedings of the American Mathematical Society, 69, 135-142.

[2] Kobayashi, M. (1981) -Submanifolds of Sasakian Manifold. Tensor, N. S., 35, 297-307.

[3] Yano, K. and Kon, M. (1989) On Contact -Submanifolds. Journal of the Korean Mathematical Society, 26, 231-262.

[4] Oubina, J.A. (1985) New Class of Almost Contact Metric Structures. Publicationes Mathematicae Debrecen, 32, 187-193.

[5] Janssens, D. and Vanhecke, L. (1981) Almost Contact Structures and Curvature Tensors. Kodai Mathematical Journal, 1, 1-27. http://dx.doi.org/10.2996/kmj/1138036310

[6] Bejancu, A. and Papaghuic, N. (1984) -Submanifolds of a Kenmotsu Manifold. Rendiconti di Matematica, 7, 607-622.

[7] Shahid, M.H. (1991) -Submanifolds of a Trans-Sasakian Manifold. Indian Journal of Pure and Applied Mathematics, 22, 1007-1012.

[8] Shahid, M.H. (1994) -Submanifolds of a Trans-Sasakian Manifold II. Indian Journal of Pure and Applied Mathematics, 25, 299-307.

[9] Al-Solamy, F.R. (2002) -Submanifolds of a Nearly Trans-Sasakian Manifold. IJMMS, 31, 167-175.

[10] Ahmad, M., Ozgür, C. and Haseeb, A. -Submanifolds of an -Sasakian Manifold with a Semi-Symmetric Metric Connection. Hacettepe Journal of Mathematics and Statistics.?

[11] Das, L.S. and Ahmad, M. (2009) -Submanifolds of an -Sasakian Manifold with a Quarter Symmetric NonMetric Connection. Mathematical Sciences Research Journal, 13, 161-169.

[12] Das, L.S., Ahmad, M. and Haseeb, A. (2011) Semi-Invariant Submanifolds of a Nearly Sasakian Manifold Endowed with a Semi-Symmetric Non-Metric Connection. Journal of Applied Analysis, 17, 1-12.

[13] Tripathi, M.M. (2004) On Semi-Invariant Submanifolds of Nearly Trans-Sasakian Manifolds. The International Journal of Pure and Applied Mathematical Sciences, 1, 15-34.

[14] Golab, S. (1975) On Semi-Symmetric and Quarter Symmetric Linear Connections. Tensor, N. S., 29, 249-254.

[15] Blair, D.E. (1976) Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics. Vol. 509, SpringerVerlag, Berlin.

[16] Gray, A. and Hervella, L.M. (1980) The Sixteen Classes of Almost Hermitian Manifolds and Their Linear Invariants. Annali di Matematica Pura ed Applicata, 4, 35-58. http://dx.doi.org/10.1007/BF01796539

[17] Blair, D.E. and Oubina, J.A. (1990) Conformal and Related Changes of Metric on the Product of Two Almost Contact Metric Manifolds. Publications Mathematiques, 34, 199-207.

http://dx.doi.org/10.5565/PUBLMAT_34190_15

[18] Gherghe, C. (2000) Harmonicity on Nearly Trans-Sasaki Manifolds. Demonstratio Mathematica, 33, 151-157.

[19] Blair, D.E., Showers, D.K. and Yano, K. (1996) Nearly Sasakian Structures. Kodai Mathematical Journal, 27, 175-180.