论文标题
逆向伪赫斯歧管及其相关的泊松结构
Contravariant Pseudo-Hessian manifolds and their associated Poisson structures
论文作者
论文摘要
违反伪赫西安歧管是赋予一对$（\ nabla，h）$的歧管$ m $，其中$ \ nabla $是平坦的连接，$ h $是一种对称的对称的bivector场，满足了contravariant codazzi方程。当$ h $可逆时，我们恢复了已知的伪赫斯歧管概念。 逆伪伪歧管具有类似于泊松歧管的属性，实际上，与任何违反伪伪歧管$（m，\ nabla，h）$我们自然地在$ tm $上进行了泊松张量。我们研究了这些属性，并详细研究了许多此类结构的类别，以强调这些流形的几何形状的丰富性。
A contravariant pseudo-Hessian manifold is a manifold $M$ endowed with a pair $(\nabla,h)$ where $\nabla$ is a flat connection and $h$ is a symmetric bivector field satisfying a contravariant Codazzi equation. When $h$ is invertible we recover the known notion of pseudo-Hessian manifold. Contravariant pseudo-Hessian manifolds have properties similar to Poisson manifolds and, in fact, to any contravariant pseudo-Hessian manifold $(M,\nabla,h)$ we associate naturally a Poisson tensor on $TM$. We investigate these properties and we study in details many classes of such structures in order to highlight the richness of the geometry of these manifolds.
