Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds

For a $$2n+1$$ -dimensional compact Sasakian manifold, if $$n\ge 2$$ , we prove that the analytic germ of variety representations fundamental group at every semi-simple representation is quadratic. To this result, almost-formality de Rham complex manifold with values in flat vector bundle. By almost-formality, also vanishing theorem on cup product cohomology bundles over manifold.