An example of harmonic map into the spheres with the singularity of order 4

Abstract

The radial map w(x)=x||x|| is well known as harmonic map into the sphere with a point singularity. Misawa and Nakauchi (0000) gave two examples of harmonic maps with the singularities xixj||x||2 and xixjxk||x||3 at x=0 respectively. In this paper we give a new example of harmonic maps into the spheres. It has the singularity xixjxkxl||x||4 at x=0.