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

The radial map w(x) = x/parallel to x parallel to 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 singularitiesand x(i)x(j)/parallel to x parallel to(2) and x(i)x(j)x(k)/parallel to x parallel to(3) at x = 0 respectively. In this paper we give a new example of harmonic maps into the spheres. It has the singularity x(i)x(j)x(k)x(l)/parallel to x parallel to(4) at x = 0. (C) 2020 Elsevier B.V. All rights reserved.