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 x i x j | | x | | 2 and x i x j x k | | x | | 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 | | x | | 4 at x = 0 .

中文翻译：

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4阶奇异球体调和映射的例子

摘要 径向图 w ( x ) = x | | × | | 众所周知，调和映射到具有点奇点的球体。Misawa 和 Nakauchi (0000) 给出了两个奇点 xixj | 调和映射的例子。| × | | 2 和 xixjxk | | × | | 3 在 x = 0 分别。在本文中，我们给出了球体调和映射的新示例。它具有奇点 xixjxkxl | | × | | 4 在 x = 0 。