A characterization of Sasakian space forms by the spectrum

We consider the problem of characterizing Sasakian manifolds of constant φφ-sectional curvature by using the spectrum 2Spec2Spec of the Laplace–Beltrami operator acting on 2-forms. In particular, we show that the sphere S2n+1S2n+1, equipped with a Berger-Sasakian metric, is characterized by its 2Spec2Spec in the class of all compact simply connected Sasakian manifolds.