摘要
设Msm(c)是等距浸入在2m-1维不定度量空间形式Ns2m-1((?))(c<(?))中的m维不定度量空间形式.若Msm(c)是极小的,我们证明Msm必定是有同一个指标s的2m-1维伪球面中的平坦子流形.我们还用孤立子理论给出了Ns2m-1中平坦的指标为s的子流形与系统之间的对应.
Let Ms^m(c) be an m-dimensional indefinite space form isometrically immersed in a (2m- 1)-dimensional indefinite space form Ns^2m-1(5) (c ^-)(c〈c^-). If Ms^m(c) is minimal, we prove that Ms^m must be flat with index s in a (2m-1)-pseudo-sphere with the same index. We also use techniques from soliton theory to get the correspondence between a kind of flat m-dimensional submanifolds with index s in the (2m-1)-dimensional pseudo-sphere Ns^2m-1 and the O(2m,s)/(O(m,s)×O(m)-system.I.
出处
《数学进展》
CSCD
北大核心
2005年第6期693-706,共14页
Advances in Mathematics(China)
基金
This work is partially supported by the National Natural Sciences Foundation of China under the projects(No.19871001,No.10271004)and(No.10131020).