S1不变扩张解及S1不变G扩张解的显式构造

Explicit Construction for S1 Invariant Extended Solution and S1 Invariant Gextended Solution

摘要:

研究了从单连通区域ΩR2∪{∞}到酉群及其实形式的调和映射的S1不变扩张解，证明了S1不变扩张解既是KerAφz可交换的又是ImAφz可交换的；给出了S1不变扩张解的另一种代数构造方法，并且证明了经过旗变换得到的扩张解仍然是S1不变的．随后给出了S1不变G扩张解的显式构造.

Abstract:

A study is made of the S1invariant extended solutions of the harmonic maps from a simply connected domain ΩR2 ∪{∞} into the unitary group U(N) (or its real form).S1invariant extended solutions prove to be not only KerAφzinvariant extended solution,but also ImAφzinvariant extended solution.Then another algebraic way to construct S1invariant extended solution is given.It is proved that the extended solution obtained by the flag transformation is also S1invariant. The explicit construction of S1invariant Gextended solution is also presented .