Mathematical Research Letters

Volume 14, Issue 4, July 2007 pp. 703-710.

Embeddings of compact Sasakian manifolds

Authors: Liviu Ornea (1) and Misha Verbitsky (2)
Author institution: University of Bucharest (1) and University of Glasgow (2)

Summary: 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 K\"ahler geometry: given a compact K\"ahler manifolds $X\subset Y$, and a K\"ahler form $\omega_X$ on $X$ which lies in a K\"ahler class $[\omega]$ of $Y$ restricted to $X$, $\omega_X$ can be extended to a K\"ahler form $\omega_Y$ on $Y$.

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