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 JAMP  Vol.6 No.2 , February 2018
Chen’s Inequalities for Submanifolds in (ĸ, &#181)-Contact Space Form with a Semi-Symmetric Non-Metric Connection
Abstract: In this paper, we obtain Chen’s inequalities in (kμ)-contact space form with a semi-symmetric non-metric connection. Also we obtain the inequalites for Ricci and K-Ricci curvatures.
Cite this paper: Ahmad, A. , Shahzad, F. and Li, J. (2018) Chen’s Inequalities for Submanifolds in (ĸ, &#181)-Contact Space Form with a Semi-Symmetric Non-Metric Connection. Journal of Applied Mathematics and Physics, 6, 389-404. doi: 10.4236/jamp.2018.62037.
References

[1]   Friedmann, A. and Schouten, J.A. (1924) über die gecmetrie der. halbsymmerischen übertragung. Mathematische Zeitschrift, 21, 211-233.
https://doi.org/10.1007/BF01187468

[2]   Hayden, H.A. (1932) Subspaces of a Space with Torsion. Proceedings of the London Mathematical Society, 34, 27-50.
https://doi.org/10.1112/plms/s2-34.1.27

[3]   Yano, K. (1970) On Semi-Symmetric Metric Connection. Revue Roumaine de Mathématique Pures et Appliquées, 15, 1579-1586.

[4]   Nakao, Z. (1976) Submanifolds of a Riemannian Manifold with Semi-Symmetric Metric Connection. Proceedings of the American Mathematical Society, 54, 261-266.
https://doi.org/10.1090/S0002-9939-1976-0445416-9

[5]   Prvanovic, M. (1975) Pseudo Metric Semi-Symmetric Connections. Publications de l’Institut Mathématique, Nouvelle Série, 18, 157-164.

[6]   Smaranda, D. and Andonie, O.C. (1976) On Semi-Symmetric Non-Metric Connection. Ann. Fac. Sci. Univ. Nat. Zaire (Kinshasa) Sect. Math.-Phys, 2, 265-270.

[7]   Agashe, N.S. and Chafle, M.R. (1992) A Semi-Symmetric Non-Metric Connection on a Riemannian Manifold. Indian Journal of Pure and Applied Mathematics, 23, 399-409.

[8]   Sengupta, J., De, U.C. and Binh, T.Q. (2000) On a Type of Semi-Symmetric Non-Metric Connection on a Riemannian Manifold. Indian Journal of Pure and Applied Mathematics, 31, 1659-1670.

[9]   Özgür, C. (2010) On Submanifolds of a Riemannian with a Semi-Symmetric Non-Metric Connection. Kuwait Journal of Science, 37, 17-30.

[10]   Chen, B.-Y. (1998) Strings of Riemannian Invariants, Inequalities, Ideal Immersions and Their Applications. The Third Pacific Rim Geometry Conference, Monogr. Geom. Topology 25. Int. Press, Cambridge, 7-60.

[11]   Chen, B.-Y. (2008) &-Invariants, Inequalities of Submanifolds and Their Applications. Topics in Differential Geometry, Editura Academiei Romane, Bucharest, 29-155.

[12]   Chen, B.-Y. (1993) Some Pinching and Classification Theorems for Minimal Submanifolds. Arch Math, 60, 568-578.
https://doi.org/10.1007/BF01236084

[13]   Arsalan, K.R., Ezentas, M.I., Murathan, C. and Özgür, B.Y. (2001) Chen Inequalities for Submanifolds in Locally Conformal Almost Cosymplectic Manifolds. Bulletin of the Institute of Mathematics Academia Sinica, 29, 231-242.

[14]   Tripathi, M.M., Kim, J.-S. and Choi, J. (2004) Ricci Curvature of Submanifolds in Locally Conformal Almost Cosymplectic Manifolds. Indian Journal of Pure and Applied Mathematics, 35, 259-271.

[15]   Matsumoto, K., Mihai, I. and Oiagă, A. (2001) Ricci Curvature of Submanifolds in Complex Space Forms. Revue Roumaine des Mathematiques Pures et Appliquees, 46, 775-782.

[16]   Mihai, A. (2006) Modern Topics in Submanifold Theory. Editura Universităti din Bucuresti, Bucharest.

[17]   Oiagă, A., Mihai, I. and Chen, B.Y. (1999) Inequalities for Slant Submanifolds in Complex Space Forms. Demonstratio Mathematica, 32, 835-846.
https://doi.org/10.1515/dema-1999-0420

[18]   Agashe, N.S. and Chafle, M.R. (1994) On Submanifolds of a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection. Tensor, 55, 120-130.

[19]   Chen, B.-Y. (1999) Relations between Ricci-Curvature and Shape Operator for Submanifolds with Orbitrary Codimentions. Glasgow Mathematical Journal, 41, 33-41.
https://doi.org/10.1017/S0017089599970271

[20]   Koufogiorgos, T. (1997) Contact Riemannian Manifolds with Constant φ-Sectional Curvature. Tokyo Journal of Mathematics, 20, 13-22.
https://doi.org/10.3836/tjm/1270042394

[21]   Arslan, K., Ezentas, R., Mihai, I., Murathan, C. and Özgür, C. (2001) Certain Inequalities for Submanifolds in (k, µ)-Contact Space Forms. Bulletin of the Australian Mathematical Society, 64, 201-212.
https://doi.org/10.1017/S0004972700039873

[22]   Zhang, P., Zhang, L. and Song, W. (2014) Chen’s Inequalities for Submanifolds of a Riemannian Manifold of Quasi-Constant Curvature with a Semi-Semmetric Metric Connection. Taiwanese Journal of Mathematics, 18, 1841-1862.
https://doi.org/10.11650/tjm.18.2014.4045

 
 
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