|
- 2016
局部对称伪黎曼流形中的2-调和类时子流形
|
Abstract:
摘要: 利用活动标架法,研究了局部对称伪黎曼流形中的2-调和类时子流形,得到了这类子流形的Simons型积分不等式以及关于其第二基本形式模长平方的拼挤定理。
Abstract: Based on the moving frames, the 2-harmonic timelike submanifolds in locally symmetric pseudo-Riemannian manifolds is studied. Also, an integral inequality of Simonss type and a pinching theorem about the squared norm of the second fundamental form in this submanifolds are obtained
[1] | EELLS J, LEMAIRE L. Selected topics in harmonic maps[M]. Washington: American Mathematical Society, 1983. |
[2] | 李影, 宋卫东. 局部对称伪Riemann流形中的紧致极大类时子流形[J]. 吉林大学学报(理学版), 2015, 53(3):457-460. LI Ying, SONG Weidong. Maximum timelike submannifold in a locally symmetric pseudo-Riemannian manifold[J]. Journal of Jilin University(Science Edition), 2015, 53(3):457-460. |
[3] | GOLDBERG S I. Curvature and homology[M]. London: Academic Press, 1962. |
[4] | 宋卫东, 江桔丽. 关于局部对称伪黎曼流形中的2-调和类空子流形[J]. 系统科学与数学, 2007, 27(2):170-176. SONG Weidong, JIANG Juli. On 2-harmonic space-like submanifolds of a locally symmetric pseudo-Riemannian manifold[J]. Journal of Systems Science and Complexity, 2007, 27(2):170-176. |
[5] | 沈一兵. 关于伪 Riemmann流形的极大子流形[J]. 杭州大学学报(自然科学版), 1991, 18(4):371-376. SHEN Yibing. On maximal submanifolds in pseudo-Riemannian manifolds[J]. Journal of Hangzhou University(Natural Science), 1991, 18(4):371-376. |
[6] | 胡有婧, 纪永强. de Sitter空间中的紧致极大类时子流形[J]. 吉林大学学报(理学版), 2014, 52(5):895-900. HU Youjing, JI Yongqiang. The compact timelike submanifolds in the de Sitter space[J]. Journal of Jilin University(Science Edition), 2014, 52(5):895-900. |
[7] | 欧阳崇珍. 伪黎曼空间型的2-调和类空子流形[J]. 数学年刊, 2000, 21(6):649-654. OUYANG Chongzhen. On 2-harmonic space-like submanifolds in pseudo-Riemannian manifolds[J]. Chinese Annals of Mathematics, 2000, 21(6):649-654. |