Research Article
Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection
Abstract
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.
References
- [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.
Year 2019,
, 102 - 110, 27.03.2019
Abstract
References
- [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.
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 27, 2019 |
| Published in Issue | Year 2019 |