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- 2017
具有半对称度量联络拟常曲率空间中子流形的Casorati曲率不等式
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Abstract:
摘要： 利用一个新的代数不等式, 对具有半对称度量联络拟常曲率空间中的子流形建立了两个关于广义标准δ-Casorati 曲率的不等式。
Abstract: By using a new algebraic inequality, we obtain two inequalities for generalized normalized Casorati curvatures of submanifolds in a Riemanian manifold of quasi-constant curvature with a semi-symmetric metric connection
| [1] | DECU S, HAESEN S, VERSTRAELEN L. Optimal inequalities characterising quasi-umbilical submanifolds[J]. J Inequal Pure Appl Math, 2008, 9(3):1-7. |
| [2] | SLESAR V, SAHIN B, V(＾overI)LCU G E. Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms[J]. Journal of Inequalities and Applications, 2014, 2014(1): 123. |
| [3] | LEE C W, YOON D W, LEE J W. Optimal inequalities for the Casorati curvatures of submanifolds of real space forms endowed with semi-symmetric metric connections[J]. Journal of Inequalities and Applications, 2014, 2014(1):327. |
| [4] | IMAI T. Notes on semi-symmetric metric connections[J]. Tensor NS, 1972, 24:293-296. |
| [5] | BLAIR D. Quasi-umbilical, minimal submanifolds of Euclidean space[J]. Simon Stevin, 1977, 51:3-22. |
| [6] | LI Guanghan, WU Chuanxi. Slant immersions of complex space forms and Chen’s inequality[J]. Acta Mathematica Scientia, 2005, 25B(2):223-232. |
| [7] | LI Xingxiao, HUANG Guangyue, XU Jiaolou. Some inequalities for submanifolds in locally conformal almost cosymplectic manifolds[J]. Soochow Journal of Mathematics, 2005, 31(3): 309-319. |
| [8] | LIU Ximin, DAI Wanji. Ricci curvature of submanifolds in a quaternion projective space[J]. Commun Korean Math Soc, 2002, 17(4):625-634. |
| [9] | OPERA T. Chens inequality in lagrangian case[J]. Colloq Math, 2007, 108(1):163-169. |
| [10] | YANO K. On semi-symmetric metric connection[J]. Revue Roumaine de Mathmatique Pures et Appl, 1970, 15:1579-1586. |
| [11] | DECU S, HAESEN S, VERSTRAELEN L. Optimal inequalities involving Casorati curvatures[J]. Bull Transylv Univ Brasov, Ser B, 2007, 14(49):85-93. |
| [12] | LEE J W, V(＾overI)LCU G E. Inequalities for generalized normalized <i>δ-</i>Casorati curvatures of slant submanifolds in quaternionic space forms[J]. Taiwanese Journal of Mathematices, 2015, 19(3):691-702. |
| [13] | NAKAO Z. Submanifolds of a Riemannian manifolds with semi-symmetric metric connections[J]. Proceedings of the AMS, 1976, 54:261-266. |
| [14] | CHEN Bangyen. Mean curvature and shape operator of isometric immersions in real-space-forms[J]. Glasgow Mathematical Journal, 1996, 38(1):87-97. |
| [15] | LEE J W, LEE C W, YOON D W. Inequalities for generalized δ-Casorati of submanifolds in real space forms endowed with semi-symmetric metric connections[J]. Revista de la Unión Matemática Argentina, 2016, 57(2):53-62. |
| [16] | ZHANG Pan, ZHANG Liang, SONG Weidong. Chens inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection[J]. Taiwanese Journal of Mathematices, 2014, 18(6):1827-1839. |
| [17] | CHEN Bangyen, YANO K. Hypersurfaces of a conformally flat space[J]. Tensor NS, 1972, 26: 318-322. |
