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从不定度量空间形式到不定度量空间形式的等距浸入(英文)

Isometric Immersions of Indefinite Space Forms in Indefinite Space Forms
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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).
关键词 空间形式 不定度量空间形式 外正交 极小浸入 space form indefinite space form exteriorly orthogonal minimal
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