Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds

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We show that the Malcev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n≥ 2 admits a quadratic presentation by using Morgan's bigradings of minimal models of mixed-Hodge diagrams. By using bigradings of minimal models, we also simplify the proof of the result of Cappelletti-Montano, De Nicola, Marrero and Yudin on Sasakian nilmanifolds.