论文标题
核心亚频泊泊术
The Poisson saturation of coregular submanifolds
论文作者
论文摘要
本文致力于泊松几何形状中的核心尺寸。我们表明他们的局部泊松饱和度是一个嵌入式泊松submanifold，我们为围绕Coregular Submanifold的Poisson Submanifold提供了正常的形式。该结果恢复了泊松横向周围的正常形式，并产生了在符号几何形状中恒定等级亚策略周围某些正常形式/刚度结果的泊松版本。作为一种应用，我们证明了关于泊松歧管中狄拉克歧管的共同体嵌入的唯一性结果。我们还展示了我们的结果如何推广到dirac几何形状中核心尺寸的设置。
This paper is devoted to coregular submanifolds in Poisson geometry. We show that their local Poisson saturation is an embedded Poisson submanifold, and we give a normal form for this Poisson submanifold around the coregular submanifold. This result recovers the normal form around Poisson transversals, and it yields Poisson versions of some normal form/rigidity results around constant rank submanifolds in symplectic geometry. As an application, we prove a uniqueness result concerning coisotropic embeddings of Dirac manifolds in Poisson manifolds. We also show how our results generalize to the setting of coregular submanifolds in Dirac geometry.
