A characterization of Sasakian space forms by the spectrum

Abstract

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