E. Loubeau et C. Oniciuc


Titre: "On the biharmonic and harmonic indices of the Hopf map."


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 $\psi:\S^3\to \S^2$ and modify it into a nonharmonic biharmonic map $\phi:\S^3\to \S^3$. We show $\phi$ 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.