TY  - JOUR
T1  - Chen Inequalities for Submanifolds of Real Space Forms with a Ricci Quarter-Symmetric Metric Connection
AU  - Poyraz, Nergiz (önen)
AU  - Yoldaş, Halil İbrahim
PY  - 2019
DA  - March
DO  - 10.36890/iejg.545850
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 102
EP  - 110
VL  - 12
IS  - 1
LA  - en
AB  - In this paper, we establish some inequalities for submanifolds of real space forms endowedwith a Ricci quarter-symmetric metric connection. Using these inequalities, we obtain the relationbetween Ricci curvature, scalar curvature and the mean curvature endowed with the Ricci quartersymmetricmetric connection.
KW  - Chen inequality
KW  - Ricci quarter-symmetric metric connection
KW  - Ricci curvature
CR  - [1] Chen, B. Y., Mean curvature and shape operator of isometric immersion in real space forms. Glasgow Mathematic Journal 38 (1996), 87-97.
CR  - [2] Chen, B. Y., Relation between Ricci curvature and shape operator for submanifolds with arbitrary codimension. Glasgow Mathematic
Journal 41 (1999), 33-41.
CR  - [3] Chen, B. Y., Some pinching and classification theorems for minimal submanifolds. Arch. math (Basel) 60 (1993), no. 6, 568-578.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [7] Hong, S. and Tripathi, M. M., On Ricci curvature of submanifolds. Int J. Pure Appl. Math. Sci. 2 (2005), no.2, 227-245.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [11] Mishra, R. S. and Pandey, S. N., On quarter symmetric metric F-connections. Tensor (N.S.) 34 (1980), no. 1, 1-7.
CR  - [12] Rastogi, S. C., On quarter-symmetric metric connection. C. R. Acad. Bulgare Sci 31 (1978), no. 7, 811-814.
CR  - [13] Tripathi, M. M., Improved Chen-Ricci inequality for curvature-like tensor and its applications. Differential Geom. Appl. 29 (2011), 685-698.
UR  - https://doi.org/10.36890/iejg.545850
L1  - https://dergipark.org.tr/en/download/article-file/681892
ER  -