Embeddings of compact Sasakian manifolds

Let $M$ be a compact Sasakian manifold. We show that $M$ admits a CR-embedding into a Sasakian manifold diffeomorphic to a sphere, and this embedding is compatible with the respective Reeb fields. We argue that a stronger embedding theorem cannot be obtained. We use an extension theorem for Kähler geometry: given a compact Kähler manifolds $X\subset Y$, and a Kähler form $\omega_X$ on $X$ which lies in a Kähler class $[\omega]$ of $Y$ restricted to $X$, $\omega_X$ can be extended to a Kähler form $\omega_Y$ on $Y$.

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Published 1 January 2007