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

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