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# Mathematical Research Letters

## Volume 14 (2007)

### Number 4

### Embeddings of compact Sasakian manifolds

Pages: 703 – 710

DOI: http://dx.doi.org/10.4310/MRL.2007.v14.n4.a15

#### Authors

#### Abstract

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 $Y$.