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Mixed Hodge structures and Sullivan’s minimal models of Sasakian manifolds. (Structures de Hodge mixtes et modèles minimaux de Sullivan des variétés sasakiennes.) (English. French summary) Zbl 1403.53040
Let $$M$$ be a compact $$(2n+1)$$-dimensional Sasakian manifold with $$n\geq 2$$. In the present work, the author proves that the Malčev Lie algebra of the fundamental group $$\pi_1(M)$$ admits a quadratic presentation, i.e., is a quotient of a free Lie algebra by an ideal generated in degree two. The proof of this result is mainly based on a clever usage of Morgan’s techniques of mixed Hodge diagrams. With the same ingredient, it is proved that a compact $$(2n+1)$$-dimensional nilmanifold admits a Sasakian structure if and only if it is a Heisenberg nilmanifold $$H_{2n+1}/\Gamma$$.

##### MSC:
 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 55P62 Rational homotopy theory 58A14 Hodge theory in global analysis
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##### References:
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