Abstract
It is known that a compact symplectic manifold endowed with a prequantum line bundle can be embedded in the projective space generated by the eigensections of low energy of the Bochner Laplacian acting on high $p$-tensor powers of the prequantum line bundle. We show that the Fubini-Study forms induced by these embeddings converge at speed rate $1/p^{2}$ to the symplectic form. This result implies the generalization to the almost-K\"ahler case of the lower bounds on the Calabi functional given by Donaldson for K\"ahler manifolds, as shown by Lejmi and Keller.
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