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Abstract <p> The present paper shows that every polarized Poisson manifold admits a torsion-free connection that preserves the foliation. Moreover, each leaf of this foliation carries a flat, torsion-free connection, which equips it with a locally affine structure. Besides, we prove Darboux’s theorem for a coisotropic foliation with respect to a polarized Poisson manifold. </p>

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Some Structures on Polarized Poisson Manifolds

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • S. El Amine,
  • I. Benali

摘要

Abstract

The present paper shows that every polarized Poisson manifold admits a torsion-free connection that preserves the foliation. Moreover, each leaf of this foliation carries a flat, torsion-free connection, which equips it with a locally affine structure. Besides, we prove Darboux’s theorem for a coisotropic foliation with respect to a polarized Poisson manifold.