A stationary harmonic map with a nonstationary tangent map

We construct a stationary weakly harmonic map from a domain in \R^5 into a compact Kähler surface for which a tangent map is weakly harmonic but nonstationary. The target manifold is the blow-up of \CP^1\times\CP^1 at four points lying in one fiber and arranged at the vertices of a regular tetrahedron. The nonstationarity of the tangent map arises from the break down of the tetrahedral symmetry in the defect measure concentrated on the vertices.