Nearly Kählerian embeddings of symplectic manifolds
Let \(X,\omega\) be a \(2n\)-dimensional compact symplectic manifold without boundary, \(H_k \subset C^\infty (X,L^{\otimes k})\) a suitable sequence of finite dimensional Hilbert spaces defined for all sufficiently large \(k\). This paper studies the asymptotic geometry of the maps \(F_k:X \to\mathbb{P} H_k^*\) obtained by the usual procedure of algebraic geometry. It is shown that the \(F_k\) are projective embeddings which for large \(k\) are `nearly' symplectic as well as `nearly' isometric. The proof parallels that of \textit{S. Zelditch} [Int. Math. Res. Not. 1998, No. 6, 317-331 (1998; Zbl 0922.58082)] to some extent.
scientific article; zbMATH DE number 1585248