Equivariant harmonic maps of the quaternionic projective spaces into Grassmannians

Source abstract

We show the rigidity of Sp(m+1)-equivariant harmonic maps from the quaternionic projective space HPm into a complex Grassmann manifold Grp(Cp+q) when q is less than 2m. Our method depends on the differential geometry of vector bundles and connections; a generalization of the do Carmo–Wallach theory based on a generalization of Takahashi’s theorem implies the result. We also obtain the rigidity of those maps into the real or quaternionic Grassmannians.