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Harmonic maps from $\mathbb{S}^{2n+1}$ to $\mathbb{C}P^n$ with low Morse index
We study the Jacobi spectrum and low-index rigidity of complex Hopf fibrations. We first give a representation-theoretic description of the Jacobi operator of a homogeneous Riemannian fibration and apply it to \[ π:(\mathbb{S}^{2n+1},g_ε)\longrightarrow(\mathbb{C}P^n,h), \] where $g_ε$ is a Berger
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