A characterization of Sasakian space forms by the spectrum

Abstract

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