Some Theorems About Unitons of Harmonic Maps into U(N)

By using the simplified method of factorization given by Valli, and the correspondence between the harmonic map φ∶S 2→U(N) and U(N) uniton bundle ν(φ) with energy corresponding to the bundles' second Chern class, which is established by Anand, the energy in a case φ∶S 2→U(N) is investigated in order to estimate the energy of a uniton using the uniton number. It is proved that Uhlenbeck's factorization is energy decreasing. And a method of estimating the energy of a uniton by the uniton number is given.