Embeddings of compact Sasakian manifolds

Liviu Ornea; Misha Verbitsky

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Embeddings of compact Sasakian manifolds

Liviu Ornea·Misha Verbitsky

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

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BibTeX RIS

Liviu Ornea, Misha Verbitsky. 2007-04-07. Embeddings of compact Sasakian manifolds. https://arxiv.org/abs/math/0609617

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