Equivariant harmonic maps of the complex projective spaces into the quaternion projective spaces

Abstract

We classify equivariant harmonic maps of the complex projective spaces $C{P}^m$ into the quaternion projective spaces. To do this, we employ differential geometry of vector bundles and connections. When the domain is the complex projective line, we have one parameter family of those maps. (This result is already shown in [2] and [4] in other ways). However, when $m\geqq 2$, we will obtain the rigidity results.