Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold with Semi-Symmetric Metric Connection

Year 2017, Volume: 10 Issue: 1, 1 - 14, 30.04.2017

Nergiz Önen Poyraz , Burçin Doğan , Erol Yaşar

https://doi.org/10.36890/iejg.584434

Cited By: 8

Abstract

Keywords

Chen inequality, lightlike hypersurface, Lorentzian manifold, semi-symmetric metric connection

References

• [1] Atindogbe, C. and Duggal, Krishan L., Conformal screen on lightlike hypersurfaces. Int. J. Pure Appl. Math., 11(2004),4,421-442.
• [2] Beem, J. K., Ehrlich, P. E., Easley, K. L., Global Lorentzian Geometry. Dekker, New York, 1996.
• [3] Bejan, C. L. and Duggal, Krishan L., Global lightlike manifolds and harmonicity. Kodai Math. J., 28(2005), 1, 131-145.
• [4] Chen, B. Y., Mean curvature and shape operator of isometric immersion in real space forms. Glasgow Mathematic Journal, 38 (1996), 87-97.
• [5] Chen, B. Y., Relation between Ricci curvature and shape operator for submanifolds with arbitrary codimension. Glasgow Mathematic Journal, 41(1999), 33-41.
• [6] Chen, B. Y., Some pinching and classification theorems for minimal submanifolds. Arch. math. (Basel), 60(1993), 6, 568-578.
• [7] Chen, B. Y., A Riemannian invariant and its applications to submanifold theory. Result Math., 27(1995), 17-26.
• [8] Chen, B. Y., Dillen, F., Verstraelen L. and Vrancken, V., Characterizations of Riemannian space forms, Einstein spaces and conformally flat spaces. Proc. Amer. Math. Soc., 128(2000),589-598.
• [9] Chen, B. Y., A Riemannian invariant for submanifolds in space forms and its applications. Geometry and Topology of submanifolds V I; (Leuven, 1993=Brussels; 193), (NJ:Word Scientific Publishing ,River Edge), 1994, pp.58 􀀀 81, no.6; 568 - 578.
• [10] Duggal, Krishan L., On scalar curvature in lightlike geometry. Journal of Geometry and Physics, 57(2007), 2, 473-481.
• [11] Duggal, Krishan L. And Bejancu, A., Lightlike Submanifold of Semi-Riemannian Manifolds and Applications. Kluwer Academic Pub., The Netherlands, 1996.
• [12] Duggal, Krishan L. and ¸Sahin, B., Differential Geometry of Lightlike Submanifolds. Birkhauser Verlag AG., 2010.
• [13] Duggal, Krishan L. and Sharma, R., Semi-Symmetric metric connection in a Semi-Riemannian Manifold. Indian J. Pure appl Math., 17(1986), 1276-1283.
• [14] Gülbahar, M., Kılıç, E. and Kele¸s, S., Chen-like inequalities on lightlike hypersurfaces of a Lorentzian manifold. J. Inequal. Appl., 2013:266,18pp.
• [15] Gülbahar, M., Kılıç, E. and Kele¸s, S., Some inequalities on screen homothetic lightlike hypersurfaces of a lorentzian manifold. Taiwanese Journal of Mathematics, 17(2013), 2, 2083-2100.
• [16] Güne¸s, R., ¸Sahin, B. and Kılıç, E., On Ligtlike Hypersurfaces of a Semi-Riemannian Space Form. Turk J. Math., 27(2003), 283-297. [17] Hayden, H. A., Subspace of a space with Torsion. Proc. London Math. Soc., 34(1932), 27-50.
• [18] Hong, S., Matsumoto, K. and Tripathi, M. M., Certain basic inequalities for submanifolds of locally conformal Kaehlerian space forms. SUT J. Math., 4(2005), 1, 75-94.
• [19] Imai, T., Notes on Semi-Symmetric Metric Connection. Tensor, N.S., 24(1972), 293-296.
• [20] Imai, T., Hypersurfaces of a Riemannian Manifold with Semi-Symmetric Metric Connection. Tensor, N.S., 23(1972), 300-306.
• [21] Liu, X. and Zhou, J., On Ricci curvature of certain submanifolds in cosympletic space form. Sarajeva J. Math., 2(2006), 95-106.
• [22] Konar, A. and Biswas, B., Lorentzian Manifold that Admits a type of Semi-Symmetric Metric Connection. Bull. Cal. Math., Soc., 93(2001), No.5, 427-437.
• [23] Mihai, A. and Özgür, C., Chen inequalities for submanifolds of real space form with a semi-symmetric metric connection. Taiwanese Journal of Mathematics, 14(2010), No. 4, pp. 1465-1477.
• [24] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity. Academic Press. London, 1983.
• [25] (Önen) Poyraz, N. and Ya¸sar, E., Chen-like inequalities on lightlike hypersurface of a Lorentzian product manifold with a quartersymmetric nonmetric connection. Kragujevac Journal of Mathematics, 40 (2016), 2, 146-164.
• [26] Tripathi, M. M., Improved Chen-Ricci inequality for curvature-like tensor and its applications. Differential Geom. Appl., 29(2011), 685-698. [27] Yano, K., On Semi-Symmetric Metric Connection. Rev. Roum. Math.Pures Et Appl., 15 (1970), 1579-1586.
• [28] Yaşar, E., Çöken, A. C. and Yücesan, A., Lightlike Hypersurfaces of Semi-Riemannian Manifold with Semi-Symmetric Metric Connection. Kuweyt Journal of Science and Engineering, 34 (2007), 11-24.