A REMARK ON THE USE OF DIFFERENTIAL FORMS FOR THE SKYRME PROBLEM

We introduce a formulation of the Skyrme problem using differential fo rms. By means of this formulation, we prove first that the homothetic map between the standard three-sphere of radius R, S-R(3) subset of R- 4, and S-1(3) the unique minimizer, module isometries, of the Skyrme e nergy in its homotopy class, for any R less than some critical value R -0 is an element of (root 3/2, root 2]. We then establish a stability result for this Skyrme-form problem from which we can recover the resu lt of M. Loss and N. S. Manton which states that this homothetic map i s stable only up to R = root 2.