Embeddings of compact Sasakian manifolds

• Autores: Liviu Ornea, Misha Verbitsky
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 4, 2007, págs. 703-710
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n4.a15
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• Resumen

  • 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 $Y$.