A note on equivariant biharmonic maps and stable biharmonic maps

In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [20], [12]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from a 4-dimensional space form into a 4-dimensional model space. We also give an improved second variation formula for biharmonic maps into a space form and use it to prove that there exists no stable proper biharmonic map with constant square norm of tension field from a compact Riemannian manifold without boundary into a space form of positive sectional curvature.