Embeddings of compact Sasakian manifolds

Details Embeddings of compact Sasakian manifolds Embeddings of compact Sasakian manifolds

2006-09-21

arxiv.org/abs/math/0609617v2

Math. Res. Lett. 14 (2007), no. 4, 703--710.

Mathematics

Differential Geometry

11 pages, minor corrections made, orbifolds explained

Scientific paper

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 Kaehler geometry: given a compact Kaehler manifolds $X\subset Y$, and a Kaehler form $\omega$ on $X$ which lies in a Kaehler class of $Y$ restricted to $X$, $\omega$ can be extended to a Kaehler form on $Y$.

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