Abstract. Biharmonic maps are the critical points of the bienergy functional and, from this point of view, generalise harmonic maps. We consider the Hopf map ψ : S → S and modify it into a nonharmonic biharmonic map φ : S → S. We show φ to be unstable and estimate its biharmonic index and nullity. Resolving the spectrum of the vertical Laplacian associated to the Hopf map, we recover Urakawa’s determination of its harmonic index and nullity.
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