Spectral properties of the twistor fibration of a quaternion Kähler manifold (Q1569008)

The authors investigate relations between Killing vector fields and eigenforms of the Laplacian on a quaternion-Kähler manifold \(M\) using spectral properties of the Kähler-Einstein twistor space \(Z\). It is shown that the Hamiltonian of a Killing field is an eigenform of the Laplacian corresponding to a minimal non-zero eigenvalue. This result gives a quaternionic version of a famous result of Lichnerowicz and Matsushima on Kähler-Einstein geometry. Using the twistor fibration \(t: Z\to M\) some relations between the spectral geometries of \(Z\) and \(M\) are established.