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

Abstract

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.
Year 2017, Volume: 10 Issue: 1, 1 - 14, 30.04.2017
https://doi.org/10.36890/iejg.584434

Abstract

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.
There are 26 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Nergiz Önen Poyraz

Burçin Doğan

Erol Yaşar

Publication Date April 30, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

APA Poyraz, N. Ö., Doğan, B., & Yaşar, E. (2017). Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold with Semi-Symmetric Metric Connection. International Electronic Journal of Geometry, 10(1), 1-14. https://doi.org/10.36890/iejg.584434
AMA Poyraz NÖ, Doğan B, Yaşar E. Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold with Semi-Symmetric Metric Connection. Int. Electron. J. Geom. April 2017;10(1):1-14. doi:10.36890/iejg.584434
Chicago Poyraz, Nergiz Önen, Burçin Doğan, and Erol Yaşar. “Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold With Semi-Symmetric Metric Connection”. International Electronic Journal of Geometry 10, no. 1 (April 2017): 1-14. https://doi.org/10.36890/iejg.584434.
EndNote Poyraz NÖ, Doğan B, Yaşar E (April 1, 2017) Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold with Semi-Symmetric Metric Connection. International Electronic Journal of Geometry 10 1 1–14.
IEEE N. Ö. Poyraz, B. Doğan, and E. Yaşar, “Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold with Semi-Symmetric Metric Connection”, Int. Electron. J. Geom., vol. 10, no. 1, pp. 1–14, 2017, doi: 10.36890/iejg.584434.
ISNAD Poyraz, Nergiz Önen et al. “Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold With Semi-Symmetric Metric Connection”. International Electronic Journal of Geometry 10/1 (April 2017), 1-14. https://doi.org/10.36890/iejg.584434.
JAMA Poyraz NÖ, Doğan B, Yaşar E. Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold with Semi-Symmetric Metric Connection. Int. Electron. J. Geom. 2017;10:1–14.
MLA Poyraz, Nergiz Önen et al. “Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold With Semi-Symmetric Metric Connection”. International Electronic Journal of Geometry, vol. 10, no. 1, 2017, pp. 1-14, doi:10.36890/iejg.584434.
Vancouver Poyraz NÖ, Doğan B, Yaşar E. Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold with Semi-Symmetric Metric Connection. Int. Electron. J. Geom. 2017;10(1):1-14.