Araştırma Makalesi
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Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection

Yıl 2019, Cilt: 12 Sayı: 1, 102 - 110, 27.03.2019
https://doi.org/10.36890/iejg.545850

Öz

In this paper, we establish some inequalities for submanifolds of real space forms endowed
with a Ricci quarter-symmetric metric connection. Using these inequalities, we obtain the relation
between Ricci curvature, scalar curvature and the mean curvature endowed with the Ricci quartersymmetric
metric connection.

Kaynakça

  • [1] Chen, B. Y., Mean curvature and shape operator of isometric immersion in real space forms. Glasgow Mathematic Journal 38 (1996), 87-97.
  • [2] Chen, B. Y., Relation between Ricci curvature and shape operator for submanifolds with arbitrary codimension. Glasgow Mathematic Journal 41 (1999), 33-41.
  • [3] Chen, B. Y., Some pinching and classification theorems for minimal submanifolds. Arch. math (Basel) 60 (1993), no. 6, 568-578.
  • [4] Chen, B. Y., A Riemannian invariant for submanifolds in space forms and its applications. Geometry and Topology of submanifolds VI. (Leuven, 1993/Brussels, 193). (NJ:Word Scientific Publishing, River Edge). 1994, pp. 58-81, no. 6, 568-578.
  • [5] Chen, B. Y., A general optimal inequlaity for arbitrary Riemannian submanifolds. J. Ineq. Pure Appl. Math 6 (2005), no. 3, Article 77, 1-11.
  • [6] Gülbahar, M., Kılıç, E., Keleş, S. and Tripathi, M. M., Some basic inequalities for submanifolds of nearly quasi-constant curvature manifolds. Differential Geometry-Dynamical Systems. 16 (2014), 156-167.
  • [7] Hong, S. and Tripathi, M. M., On Ricci curvature of submanifolds. Int J. Pure Appl. Math. Sci. 2 (2005), no.2, 227-245.
  • [8] Kamilya, D and De, U. C., Some properties of a Ricci quarter-symmetric metric connection in a Riemanian manifold. Indian J. Pure and Appl. Math 26 (1995), no. 1, 29-34.
  • [9] Liu, X. and Zhou, J., On Ricci curvature of certain submanifolds in cosympletic space form. Sarajeva J. Math 2 (2006), no.1, 95-106.
  • [10] 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, 1465-1477.
  • [11] Mishra, R. S. and Pandey, S. N., On quarter symmetric metric F-connections. Tensor (N.S.) 34 (1980), no. 1, 1-7.
  • [12] Rastogi, S. C., On quarter-symmetric metric connection. C. R. Acad. Bulgare Sci 31 (1978), no. 7, 811-814.
  • [13] Tripathi, M. M., Improved Chen-Ricci inequality for curvature-like tensor and its applications. Differential Geom. Appl. 29 (2011), 685-698.
Yıl 2019, Cilt: 12 Sayı: 1, 102 - 110, 27.03.2019
https://doi.org/10.36890/iejg.545850

Öz

Kaynakça

  • [1] Chen, B. Y., Mean curvature and shape operator of isometric immersion in real space forms. Glasgow Mathematic Journal 38 (1996), 87-97.
  • [2] Chen, B. Y., Relation between Ricci curvature and shape operator for submanifolds with arbitrary codimension. Glasgow Mathematic Journal 41 (1999), 33-41.
  • [3] Chen, B. Y., Some pinching and classification theorems for minimal submanifolds. Arch. math (Basel) 60 (1993), no. 6, 568-578.
  • [4] Chen, B. Y., A Riemannian invariant for submanifolds in space forms and its applications. Geometry and Topology of submanifolds VI. (Leuven, 1993/Brussels, 193). (NJ:Word Scientific Publishing, River Edge). 1994, pp. 58-81, no. 6, 568-578.
  • [5] Chen, B. Y., A general optimal inequlaity for arbitrary Riemannian submanifolds. J. Ineq. Pure Appl. Math 6 (2005), no. 3, Article 77, 1-11.
  • [6] Gülbahar, M., Kılıç, E., Keleş, S. and Tripathi, M. M., Some basic inequalities for submanifolds of nearly quasi-constant curvature manifolds. Differential Geometry-Dynamical Systems. 16 (2014), 156-167.
  • [7] Hong, S. and Tripathi, M. M., On Ricci curvature of submanifolds. Int J. Pure Appl. Math. Sci. 2 (2005), no.2, 227-245.
  • [8] Kamilya, D and De, U. C., Some properties of a Ricci quarter-symmetric metric connection in a Riemanian manifold. Indian J. Pure and Appl. Math 26 (1995), no. 1, 29-34.
  • [9] Liu, X. and Zhou, J., On Ricci curvature of certain submanifolds in cosympletic space form. Sarajeva J. Math 2 (2006), no.1, 95-106.
  • [10] 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, 1465-1477.
  • [11] Mishra, R. S. and Pandey, S. N., On quarter symmetric metric F-connections. Tensor (N.S.) 34 (1980), no. 1, 1-7.
  • [12] Rastogi, S. C., On quarter-symmetric metric connection. C. R. Acad. Bulgare Sci 31 (1978), no. 7, 811-814.
  • [13] Tripathi, M. M., Improved Chen-Ricci inequality for curvature-like tensor and its applications. Differential Geom. Appl. 29 (2011), 685-698.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Nergiz (önen) Poyraz

Halil İbrahim Yoldaş

Yayımlanma Tarihi 27 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 1

Kaynak Göster

APA Poyraz, N. (., & Yoldaş, H. İ. (2019). Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection. International Electronic Journal of Geometry, 12(1), 102-110. https://doi.org/10.36890/iejg.545850
AMA Poyraz N(, Yoldaş Hİ. Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection. Int. Electron. J. Geom. Mart 2019;12(1):102-110. doi:10.36890/iejg.545850
Chicago Poyraz, Nergiz (önen), ve Halil İbrahim Yoldaş. “Chen Inequalities for Submanifolds of Real Space Forms With a Ricci Quarter-Symmetric Metric Connection”. International Electronic Journal of Geometry 12, sy. 1 (Mart 2019): 102-10. https://doi.org/10.36890/iejg.545850.
EndNote Poyraz N(, Yoldaş Hİ (01 Mart 2019) Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection. International Electronic Journal of Geometry 12 1 102–110.
IEEE N. (. Poyraz ve H. İ. Yoldaş, “Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection”, Int. Electron. J. Geom., c. 12, sy. 1, ss. 102–110, 2019, doi: 10.36890/iejg.545850.
ISNAD Poyraz, Nergiz (önen) - Yoldaş, Halil İbrahim. “Chen Inequalities for Submanifolds of Real Space Forms With a Ricci Quarter-Symmetric Metric Connection”. International Electronic Journal of Geometry 12/1 (Mart 2019), 102-110. https://doi.org/10.36890/iejg.545850.
JAMA Poyraz N(, Yoldaş Hİ. Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection. Int. Electron. J. Geom. 2019;12:102–110.
MLA Poyraz, Nergiz (önen) ve Halil İbrahim Yoldaş. “Chen Inequalities for Submanifolds of Real Space Forms With a Ricci Quarter-Symmetric Metric Connection”. International Electronic Journal of Geometry, c. 12, sy. 1, 2019, ss. 102-10, doi:10.36890/iejg.545850.
Vancouver Poyraz N(, Yoldaş Hİ. Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection. Int. Electron. J. Geom. 2019;12(1):102-10.