到一类对称空间的调和映射  

On Harmonic Maps into Some Symmetric Spaces

作　　者：贺群[1] 赵寿为[1] 

机构地区：[1]同济大学应用数学系,上海200092

出　　处：《同济大学学报（自然科学版）》2005年第2期234-237,共4页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(10471105)

摘　　要：研究从单连通区域Ω R2∪{∞}到一类对称空间———G Grassmann流形Mk(其中包括实Grassmann流形和四 元Grassmann流形)的调和映射,引入了G Grassmann uniton的概念,并通过dressing作用给出了由已知G Grassmann uniton构造新的G Grassmann uniton的方法.证明了任意具有有限uniton数的调和映射φ∶Ω→Mk可因子分解为有限 个G Grassmann uniton的乘积.最后,给出了一种到G Grassmann流形的迷向调和序列的构造方法.The harmonic maps from a simply connected domain ΩR 2∪｛∞｝ into some symmetric spaces M k ,which can be embedded into some real forms G of unitary group U(N) and contain real Grassmann manifolds and Quaternion manifolds,are studied.The G -Grassmann-uniton is introduced and constructed from a known one by the method of the dressing action.It is proved that any harmonic map φ ∶Ω→ M k with finite uniton number can be factorized into a product of a finite number of G -Grassmann-unitons.Finally,a way to construct a sequence of isotropic harmonic maps into G -Grassmann manifold is given.

关 键 词：调和映射 因子分解 G-Grassmann流形 G-Grassmann-uniton 

分 类 号：O186.16[理学—数学]