Harmonic maps from $S^3$ to $S^2$ and the rigidity of the Hopf fibration

Athanasios Georgakopoulos, Marco Magliaro, Luciano Mari +1

It was conjectured by Eells that the only harmonic maps $f:S^3\to S^2$ are Hopf fibrations composed with conformal maps of $S^2$. We support this conjecture by proving its valid…