We study coisotropic submanifolds of b-symplectic manifolds. We prove that b-coisotropic submanifolds (those transverse to the degeneracy locus) determine the b-symplectic structure in a neighborhood, and provide a normal form theorem. This extends Gotay’s theorem in symplectic geometry. Further, we introduce strong b-coisotropic submanifolds and show that their coisotropic quotient, which locally is always smooth, inherits a reduced b-symplectic structure.

中文翻译：

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b-辛几何中的各向同性子流形

我们研究b辛流形的各向同性子流形。我们证明了b -coisotropic submanifolds（那些横向于简并轨迹的）确定了邻域中的b -辛结构，并提供了一个范式定理。这扩展了辛几何中的戈泰定理。此外，我们引入了强的b -coisotropic submanifolds 并表明它们的 coisotropic 商，其局部总是平滑的，继承了减少的b -辛结构。