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

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 .