Abstract
On a quaternion-Kähler manifold M the Hamiltonian of a Killing field is a 2-form and we show it is an eigenform of the Laplacian corresponding to the minimal eigenvalue. This gives a quaternionic version of a famous result of Lichnerowicz and Matsushima on Kähler–Einstein geometry. As a main tool we use the twistor fibration t :Z→M and establish some relations between the spectral geometries of Z and M.
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