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.